Answer:
the correct answer is 15.2
What is the slope of the line passing through (-2, 4)
and (3, -4)?
Answer:
[tex]\frac{-8}{5}[/tex]
Step-by-step explanation:
Slope is the change in y over the change in x
[tex]\frac{y_{2 - y_{1} } }{x_{2 - y_{1} } }[/tex]
(-2,4) is ([tex]x_{1}[/tex], [tex]y_{1}[/tex])
(3. -4) is ([tex]x_{2}[/tex],[tex]y_{2}[/tex])
[tex]\frac{-4 - 4}{3 - -2}[/tex] = [tex]\frac{-8}{3+ 2}[/tex] = [tex]\frac{-8}{5}[/tex]
Answer:
-8 / 5
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -4 -4)/( 3 - -2)
= -8/ ( 3+2)
= -8 / 5
There are 2.54 centimeters in 1 Inch. There are 100 centimeters in 1 meter. To the nearest inch, how many inches are in 7 meters? Enter the answer in the box. inches
Based on the given equivalences, you have:
7 m = 7(100 cm) = 700 cm
700 cm = 700 (2.54 in) = 1,778 in
Hence, there are 1,778 inches in 7 meters
Use y = 3x2 + 18x - 2 to answer the following question(1, 19) is a point on the graph. What point is the reflection of (1, 19) across the axis of symmetry of the parabola?
Since y is a parabolla, there will be two values for y = 19. We already know that x = 1 is one value, to find the other, we can substitute y = 19 on the equation and solve for x to get the following:
[tex]\begin{gathered} 19=3x^2+18x-2 \\ \Rightarrow3x^2+18x-2-19=0 \\ \Rightarrow3x^2+18x-21=0 \\ \Rightarrow3(x^2+6x-7)=0 \\ \Rightarrow3(x-1)(x+7)=0 \end{gathered}[/tex]the solutions of the equation are x = 1 and x = -7. Since we already have that (1,19) is a point on the graph, then we have that the other point is (-7,19)
i need help with this asap please
Answer:
Given that,
[tex]2+(-8)+32+(-128)+.\ldots_{}[/tex]To find the sum of the first 5 terms.
First, to find the first 5 terms of the given sequence.
The given sequence is 2,-8,32,-128,...
It follows geometric series with initial term 2, and common ratio as -4
The explicit formula of the given sequence is,
[tex]t_n=2(-4)^{n-1}_{}_{}[/tex]To find the 5th term of the sequence,
Put n=5 in the above equation we get,
[tex]t_5=2(-4)^{5-1}[/tex][tex]t_5=2(-4)^4[/tex][tex]t_5=2(256)[/tex][tex]t_5=512[/tex]Since common ratio is less than 1, we get the sum of the series formula as,
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]Substituting the values we get,
[tex]S_5=\frac{2(1-(-4)^5)}{1+4}[/tex][tex]=\frac{2(1+1024)}{5}[/tex][tex]=\frac{2(1025)}{5}[/tex][tex]=2(205)[/tex][tex]=410[/tex]The sum of the first 5 terms of the given series is 410.
Answer is: option B: 410
The graph shows the reciprocal parent function.Which statement best describes the function?O A. The function is negative when x < 0.OB. The function is never negative.C. The function is negative when x > 0.O D. The function is negative when x < 0 and also when x > 0.PREVIOUS
Let's begin by identifying key information given to us in the graph:
The reciprocal parent function is given as 1/f(x). This is better written as shown below
[tex]\begin{gathered} f(x)=\frac{a}{(x-h)}+k \\ when\colon h=0,k=0,a=1 \\ f(x)=\frac{1}{x-0}+0 \\ f(x)=\frac{1}{x} \\ f(x)=y \\ \Rightarrow y=\frac{1}{x} \end{gathered}[/tex]When the value for x is greater than zero, the function is positive as shown below:
[tex]\begin{gathered} x=2 \\ y=\frac{1}{2}=\frac{1}{2} \\ y=\frac{1}{2} \end{gathered}[/tex]When the value of x is lesser than zero, the function is negative as shown below:
[tex]\begin{gathered} x=-1 \\ y=\frac{1}{-1}=-1 \\ y=-1 \end{gathered}[/tex]Therefore, the correct answer is option A (The function is negative when x < 0)
What quadrant is 0 And. . -1 1/2 in or is it on a y- axis or x-axis.
The coordinate pair is between the third and fourth quadrants, on the y-axis.
In which quadrant is the coordinate point?Remember that the quadrants are:
First quadrant: x > 0, y > 0.
Second quadrant: x < 0, y > 0.
Third quadrant: x < 0, y < 0.
Fourth quadrant: x > 0, y < 0.
In this case our coordinate pair is (0, -1/2).
So it will be between the third and fourth quadrants.
And yes, because one of the variables is zero, it is on the y-axis (just between the two quadrants).
Learn more about coordinate pairs.
https://brainly.com/question/17206319
#SPJ1
I need help with part b.
log ( √2.86668684 ) is value of logarithm 18 .
What is logarithm used for in math?
In order to get another number, a number must be raised to a certain power, which is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, the base ten logarithm of 100 is 2, since ten multiplied by two yields the number 100: log 100 = 2.The answer is found using a logarithm (or log).[tex]log_{b} \sqrt{18}[/tex] = [tex]log_{b} = log_{b} \sqrt{15} + log_{b} \sqrt{3}[/tex]
= log( √15 + √3 )
= log ( √1.0986 * 1.6094 + √1.0986 )
= log ( √1.76808684 + √1.0986 )
= log ( √2.86668684 )
Learn more about logarithm
brainly.com/question/28346542
#SPJ13
In reference to 3x + 2 ≥-4Is 0 a solution?Yes or No?
ANSWER :
yes
EXPLANATION :
From the problem, we have the inequality :
[tex]3x+2\ge-4[/tex]To check if a number is a solution, substitute it to the inequality and check the truthfulness.
Check if 0 is a solution :
[tex]\begin{gathered} 3(0)+2\ge-4 \\ 2\ge-4 \end{gathered}[/tex]Since 2 is greater than -4, therefore 0 is a solution
Help i need an answer.
The National Opinion Research Center administered the General Social Surve
persons in the United States who were 18 years of age or older. One question asked
respondents for their highest grade of school completed (Respondent's Years of Education).
Another question asked respondents for the highest grade of school that their father had
completed (Father's Years of Education).
The equation for the least squares regression line for predicting a respondent's years of
education, ý, from the years of education for the respondent's father, x, is:
ý = 9.996 + 0.355x
Predict the years of education for a person whose father had 14 years of education. Round to
the nearest whole number.
The years of education as per the given equation, for a person whose father had 14 years of education is 14.966 years.
What is education?
A planned activity, education has objectives like knowledge transmission or character and skill development. The development of understanding, reason, kindness, and honesty may be some of these goals.
As given in the question,
respondent's years of education is represented by y, and
respondent's father years of education is represented by x,
The equation for the least squares regression line for predicting a respondent's years of education is given as:
y = 9.996 + 0.355x
The year of education of respondent's father is given as 14
So putting the value of x in the given equation as 14:
we get,
y = 9.996 + 0.355(14)
y = 14.966
Hence, the years of education for a person whose father had 14 years of education is 14.966 years.
To know more about education, go to link
https://brainly.com/question/25887038
#SPJ9
When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions.
How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green? Explain or show your reasoning.
Make up a new pair of numbers that would make the same shade of green. Explain how you know they would make the same shade of green.
row 1
cups of blue paint
cups of yellow paint
row 2
2
10
row 3
1
5
row 4
3
15
What is the proportional relationship represented by this table?
What is the constant of proportionality? What does it represent?
By Calculating the Constant of Proportionality, we get,
1. 5 cups of yellow paint is required for 1 cup of blue paint.
2. For 4 cups of blue paint, 20 cups of yellow paint is required.
For 5 cups of blue paint, 25 cups of yellow paint are required.
3. Cups of Yellow Paints = 5* Cups of Blue Paints
4. The constant of Proportionality is 5.
Let the cups of blue paint = x
and cups of yellow paint = y
From the table, we can infer that to make the same shade of green, we need to mix 5 cups of yellow color with 1 cup of blue.
We have, To make the same shade of green,
we need to mix 5 cups of yellow color with 1 cup of blue.
we need to mix 10 cups of yellow color with 2 cups of blue.
we need to mix 15 cups of yellow color with 3 cups of blue.
So, here we can see a relationship between the two colors, blue (x) and green(y)
Let k be the constant of proportionality, then, we have :
10 = k *2
k =[tex]\frac{10}{2} = 5[/tex]
Hence, For one cup of blue paint, we need 5 cups of yellow paint to make the same shade of green.
And the equation of the same is y =kx, that is y =5x....equation(1)
To make new pair of numbers that would make the same shade of green.
We can use the equation 1,
for x = 4, we need y = 20
foe x =5, we need y = 25
To read more about the constant of proportionality, visit https://brainly.com/question/22620356
#SPJ1
10a-4a simplify
PLEASEE I NEED HELLPPP
they answer is 6a because you mines 10-4 and you get 6 then just put the loke 6a
20 students started the class. Then 2 students dropped the
class.
What percent of the students have dropped the class?
equati 1. v = 3.1 + 14 y = -1
y= 3x +14 (a)
y=-4x (b)
Replace the value of y (b) on equation (a), and solve for x
-4x = 3x+14
-4x-3x = 14
-7x = 14
x= 14/-7
x = -2
Replace the value of x on any initial equation and solve for y:
y= -4 (-2) = 8
y=8
Answer:
1*v=3,0.1+14y=-1 : v=3,y=-0.07857
[1.v=3}
[0.1+14y=-1]
v=3,y=-0.07857
Step-by-step explanation:
Trying to find the length of the robot arm given the xy point along with angle theta and angle theta r
8a. The length of the robot arm, and the angle in radian and degrees are as follows
length of the robot arm = 30 unitsangle in radian = 7π/6 radian (anticlockwise)angle in degrees = 210 degrees (anticlockwise)8b. The length of the robot arm, and the angle in radian and degrees are as follows
length of the robot arm = 60 unitsangle in radian = π/6 radian (clockwise)angle in degrees = 210 degrees (clockwise)How to find the length of the robot arm and the angles8a
i. let the length of the robot arm be r
The length of the lever arm using the points is done by
r^2 = ( -26 )^2 + ( -15 )^2
r^2 = 676 + 225
r^2 = 900
r = √ 900
r = 30
ii. theta in radian
tan θ = opposite / adjacent
tan θ = y direction / x direction
tan θ = -15 / -26
tan θ = 15/26
θ = Arc tan ( 15/26 )
θ = 29.9816 degrees
θ ≈ 30 degrees
θ ≈ 30 degrees + 180 = 210 degrees
In radian
π = 180 degrees
? = 210 degrees
we cross multiply to get
? * 180 degrees = π * 210 degrees
? = π * 210 degrees / 180 degrees
= 7π/6 radian
8b
i. let the length of the lever arm be r
The length of the lever arm using the points is done by
r^2 = ( -30 )^2 + ( 52 )^2
r^2 = 900 + 2704
r^2 = 3604
r = √ 3604
r = 60.033
r ≈ 60
ii. theta in radian
tan θ = opposite / adjacent
tan θ = y direction / x direction
tan θ = -30 / 52
tan θ = -30/52
θ = Arc tan ( -30/52 )
θ = -29.9816 degrees
θ ≈ -30 degrees (clockwise direction)
In radian
π = 180 degrees
? = 30 degrees
we cross multiply to get
? * 180 degrees = π * 30 degrees
? = π * 30 degrees / 180 degrees
= π/6 radian
Read more on angles here: https://brainly.com/question/25770607
#SPJ1
Which of the following is the correct mathematical expression for:
The difference between three times a number and 4
A. 3x + 4
B. 3x - 4
C. 1/3x + 4
D. 1/3x - 4
Answer:
B
Step-by-step explanation:
if the number is x then 3 times the number is 3x
the difference is the subtraction of 3x and 4 , that is
3x - 4
I BEG YOU FOR HELP!!! Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
Answer:
Step-by-step explanation:
The triangles are congruent because they follow the SSS triangle congruence postulate. As the SSS postulate says that all 3 sides of one triangle are congruent to another triangle's sides, these triangles shown have all three of their sides congruent to each other.
Answer: I am no sure but the only way to decide whether a pair of triangles are congruent would be to measure all of the sides and angles, and these triangles do not look the same so I would say that these tringles are not congruent.
Step-by-step explanation:
The nutty professor sells cashews for $6.20 per pound and Brazil nuts for $4.30 per pound. How much of each type should be used to make a 32 pound mixture that sells for $5.37 per pound?
Let's call C the weight of the Cashews and B the weight of the Brazil nuts.
Since the professor wants to sel a 32 pound mixture, we have the following equation:
[tex]C+B=32.[/tex]Now, since the price of the mixture will be $5.37 per pound, this means the price of the whole mixture will be
[tex]32\cdot5.37=171.84.[/tex]This leads us to the followin equation:
[tex]6.20C+4.30B=171.84.[/tex]Now we have a system of equations:
[tex]C+B=32[/tex][tex]6.20C+4.30B=171.84.[/tex]To solve it, let's isolate one of the variables in the first equation by subtracting B from both sides of it:
[tex]C=32-B\text{.}[/tex]Now, let's use this value of C in the second equation:
[tex]6.20(32-B)+4.30B=171.84,[/tex][tex]198.4-6.20B+4.30B=171.84,[/tex][tex]198.4-1.9B=171.84.[/tex]To solve this equation, let's subtract 198.4 from both sides of it:
[tex]-1.9B=-26.56.[/tex]Then, let's divide both sides by -1.9:
[tex]B\approx13.98.[/tex]Using this value of B in the first equation will give us:
[tex]C=32-13.98=18.02.[/tex]These would be the values of B and C round to two decimals. If we want, we can also write them as integer numbers. so the mix would need to have 18 pounds of cashews and 14 pounds of Brazil nuts.
Answer the questions below.
(a) Amount of data entered
The amount of data entered affects his pay at the end of the week.(b) R
The independent variable is the input.(c) Average temperature
The average temperature depends on the city's distance from the equator.a box contains 3 white balls and 4 black balls. a ball is drawn at random the color is recorded and then the ball is put back in the box. Then a second ball is drawn at random from the same box. find the probability of the event that at least one of the balls is white
The box has 3 white balls and 4 black balls.
Total number of balls = 3 + 4 = 7
First draw:
The probability of getting a white ball is given by
[tex]\begin{gathered} P(white)=\frac{\text{number of white balls}}{total\text{ number of balls}} \\ P(white)=\frac{3}{7} \end{gathered}[/tex]Second draw:
Notice that after the first draw the ball is put back in the box.
The probability of getting a white ball is given by
[tex]P(white)=\frac{3}{7}[/tex]At least one of the balls is white means that one white ball or two white balls.
[tex]P(x\ge1)\; =P(x=1)+P(x=2)_{}[/tex]We have already found the probability of getting one white ball that is P(x=1) = 3/7
The probability of getting two white balls is
[tex]\begin{gathered} P(two\; white)=P(white)\times P(white) \\ P(two\; white)=\frac{3}{7}\times\frac{3}{7}=\frac{9}{49} \end{gathered}[/tex]Finally, the probability of at least one white ball is
[tex]\begin{gathered} P(x\ge1)\; =P(x=1)+P(x=2)_{} \\ P(x\ge1)\; =\frac{3}{7}+\frac{9}{49} \\ P(x\ge1)\; =\frac{30}{49} \end{gathered}[/tex]Therefore, the probability of the event that at least one of the balls is white is 30/49
Hi I need help with this! I completed most of it, but I need help with the last portion. Thank you!
The equation of the axis of symmetry is x = 2
Explanation:The equation of the axis of symmetry is the value of x that divides the parabola into equal halves (mirror images).
The value of x which gives the mirror images is the value of x coordinate of the vertex. The vertex is at (2, 0). The x coordinate = 2
From the graph, we can also see it occurred at x = 2
The axis of symmetry: x = x-coordinate of the vertex
The equation of the axis of symmetry is x = 2
4. Manu determines the roots of a polynomial equation by applying the theorems he knows. He organizes the results of these theorems.
From the fundamental theorem of algebra, Manu knows there are 3 roots to the equation.
From Descartes’ rule of sign, Manu finds no sign changes in and 3 sign changes in .
The rational root theorem yields as the list of possible rational roots.
The lower bound of the polynomial is .
The upper bound of the polynomial is 1.
What values in Manu’s list of rational roots should he try in synthetic division in light of these findings?
The values in Manu’s list of rational roots he should try in the synthetic division, in light of these findings is
"Manu should try first +1/4,+1/2 and +1."
This is further explained below.
What is the synthetic division?Generally, Because the lower and higher bonds are located between -6 and 1, Manu should have only analyzed the potential rational zeros that fall between those two numbers.
A lower bond indicates that the feasible rational zero cannot be lower than -6, and therefore the higher number that may be achieved cannot be more than 1.
In this manner, Manu will get an opportunity to test. This approach of rationalization based on bonds aims to reduce the number of potential solutions.
Therefore, if Manu discovers through the synthetic division that the possible roots are +1/4,+1/2,+1,+5/4,+2,+5/2,+4,+5,+10,+20, then he should only consider those inside the intervals marked by the lower and upper bounds, which are +1/4,+1/2,+1, because the rest is greater than 1. This is because the rest of the possible roots are higher than 1.
Read more about synthetic division
https://brainly.com/question/28824872
#SPJ1
CQ
Manu determines the roots of a polynomial equation p(x)=0 by applying the theorems he knows. He organizes the results of these theorems. From the fundamental theorems of algebra, Manu knows there are 3 roots to the equation. From Descartes' rule of sign, Manu finds no sign changes in p(x) and 3 sign changes in p(-x). The rational root theorem yields +1/4,+1/2,+1,+5/4,+2,+5/2,+4,+5,+10,+20 as a list of possible rational roots. The lower bound of the polynomial is -6. The upper bound of the polynomial is 1. What values in Manu's list of rational roots should he try in synthetic division in light of these findings?
Find the area of a triangular window with the given base and height base = 10 ft height =7 ft
The area of a triangular shape is given by the following formula
[tex]A=\frac{bh}{2}[/tex]where,
base, b = 10 ft
height, h = 7 ft
therefore,
[tex]A=\frac{10\cdot7}{2}=\frac{70}{2}=35[/tex]thus, the answer is 35 ft^2
Select all the intervals where if is increasing
The given function is increasing over these following intervals:
B. -2 ≤ x ≤ -1.
C. 0 < x < 1.
Where to find where a function is increasing, from it's graph?Considering the graph of the function, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.Conversely, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when x increases, y decreases.Considering the given definitions on the bullet points above, the behavior of the function can be separated as follows:
Increasing on -2.5 ≤ x ≤ 2.5.Decreasing on all other intervals except the one above.Items B and C have subsets of the interval -2.5 ≤ x ≤ 2.5, hence the function is increasing on those intervals, and they are the correct options for this problem.
More can be learned about increasing functions at https://brainly.com/question/1503051
#SPJ1
-3-23x=-14(x-21)-15(x+33)
Find (x)
Please I keep messing up somewhere so please show step by step
The value of (x) that satisfy the equation → - 3 - 23x = - 14(x - 21) - 15(x + 33) is x = - 33.
What is Equation?
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given is the following equation -
- 3 - 23x = - 14(x - 21) - 15(x + 33)
The given equation is -
- 3 - 23x = - 14(x - 21) - 15(x + 33)
Simplifying for (x), we get -
- 3 - 23x = - 14x + 294 - 15x - 495
- 23x + 14x + 15x = 3 + 294 - 495
6x = - 198
x = - 33
Therefore, the value of (x) that satisfy the equation → - 3 - 23x = - 14(x - 21) - 15(x + 33) is x = - 33.
To solve more questions on Simplifying equations, visit the link below-
https://brainly.com/question/26127254
#SPJ1
Solve the system of inequalities by graphing.
y ≥ 2
y < 4
Select a line to change it between solid and dotted. Select a region to shade it.
The area between the solid line (y=x+4) and the dotted line (y=-2x-2) represents the system of inequalities solution set.
Two linear inequalities system on a coordinate plane. The first has a solid line graphed with a negative slope of one, a negative y-intercept, and a shaded origin area. The area encompassing the origin is shaded, and the second is a dashed vertical line 3 units to the left of the origin.
x ≥ –3; y ≥ x – 2
x > –3; 5y ≥ –4x – 10
x > –3; y ≥ –x + 1
x > –2; y ≥ –x – 1
The solution set for the system of inequalities is represented by the region between the solid line (y=x+4) and the dotted line (y=-2x-2).
Learn more about graphs at
https://brainly.com/question/7149541
#SPJ9
Suppose you buy two sweaters. Each sweater cost the same amount. The amount of money you spend varies directly with the number of sweaters you buy. If you spent $37.50 for two sweaters, what is the constant of variation? A. 2.00 B. 37.50 C. 0.053 D. 18.75
Answer:
D
Step-by-step explanation:
37.50 ÷ 2 = 18.75. jdjdjfbffcv
Question 2-22
A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eatin
5
36
35
36
O
●
cakes/week
1
01 cakes/week
35
1
1 cakes/week
4
< Previous
cakes/week
2022-2023 T-Math-Gr7Reg-T2-CBT: Section 2-...
Jake's weekly rate of eating of cake slices is 11.6
Given,
Number of equal slices of cake = 12
Number of slices Jake eaten after 3 days = 5
We have to find the weekly rate of eating;
Here,
Number of days in a week = 7
Jake eaten 5 slices in 3 days so, 7 - 3 = 4
Again after 3 days 5 slices.
Then,
4 - 3 = 1
That is, Jake eaten 10 slices of cake in 6 days.
Number of cake slices eaten in 1 day = 5/3 = 1.6
Therefore,
Weekly rate of eating is 10 + 1.6 = 11.6
That is,
Jake's weekly rate of eating of cake slices is 11.6
Learn more about rate of eating here;
https://brainly.com/question/28953060
#SPJ1
Question 1. Find the center and radius of the circunscribed circle.
In order to find the center of the circunscribed circle, we can use the midpoint theorem because the center point is in the middle of any two vertices
that is, if we take points (9,23) and (8,16) the midpoint C is given as
[tex]C=(\frac{8+9}{2},\frac{16+23}{2})[/tex]which gives
[tex]C=(8.5,19.5)[/tex]So the center of the circle is the point (8.5,19.5)
On the other hand, the radius is equal to the distance from any vertex to the center. If we take the vertex (8,16), we get
[tex]r=\sqrt[]{(8.5-8)^2+(19.5-16)^2}[/tex]which gives
[tex]\begin{gathered} r=\sqrt[]{0.5^2+3.5^2} \\ r=\sqrt[]{0.25+12.25} \\ r=\sqrt[]{12.5} \\ r=3.5355 \end{gathered}[/tex]so, the radius measure 3.54 units.
Now, lets prove that the answer are correct. In order to do that, we can choose the other vertices and apply the same procedure as above.
So the vertices are (5,20) and (12,19). Again, the center is the midpoint between these points and is given as
[tex]\begin{gathered} C=(\frac{5+12}{2},\frac{20+19}{2}) \\ C=(\frac{17}{2},\frac{39}{2}) \\ C=(8.5,19.5) \end{gathered}[/tex]which is the same center as above.
Now, the distance from the center to vertec (5,20) is
[tex]\begin{gathered} r=\sqrt[]{(8.5-5)^2+(20-19.5)^2} \\ r=\sqrt[]{3.5^2+0.5^2} \\ r=\sqrt[]{12.25+0.25} \\ r=\sqrt[]{12.5} \\ r=3.5355 \end{gathered}[/tex]which is the same radius obtained above. Then, the answers are correct.
Graph the y = 2x ^ 2 - 12x + 15 Plot five points on the parabolathe vertextwo points to the left of the vertex, and two points to the right of the vertexThen click on the graph-a-function button
Explanation:
Given the function:
[tex]y=2x^2-12x+15[/tex]First, we find the vertex of the parabola.
Vertex
The equation of the axis of symmetry is calculated using the formula:
[tex]x=-\frac{b}{2a}[/tex]From the function: a=2, b=-12
[tex]\implies x=-\frac{-12}{2(2)}=\frac{12}{4}=3[/tex]Substitute x=3 into y to find the y-coordinate at the vertex.
[tex]\begin{gathered} y=2x^2-12x+15 \\ =2(3)^2-12(3)+15 \\ =18-36+15 \\ =-3 \end{gathered}[/tex]The vertex is at (3, -3).
Two points to the left of the vertex
When x=2
[tex]\begin{gathered} y=2x^2-12x+15 \\ =2(2)^2-12(2)+15=8-24+15=-1 \\ \implies(2,-1) \end{gathered}[/tex]When x=1
[tex]\begin{gathered} y=2x^2-12x+15 \\ =2(1)^2-12(1)+15=2-12+15=5 \\ \implies(1,5) \end{gathered}[/tex]Two points to the right of the vertex
When x=4
[tex]\begin{gathered} y=2x^2-12x+15 \\ =2(4)^2-12(4)+15=32-48+15=-1 \\ \implies(4,-1) \end{gathered}[/tex]When x=5
[tex]\begin{gathered} y=2x^2-12x+15 \\ =2(5)^2-12(5)+15=50-60+15=5 \\ \implies(5,5) \end{gathered}[/tex]Answer:
Plot these points on the graph: (3, -3), (2,-1), (1,5), (4,-1), and (5,5).