(Essay Worth 10 points)
(08.01 HC)
Use the function f(x) to answer the questions:
f(x) = 5x²+2x-3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

Question

04-08-2022
Mathematics

contestada

(Essay Worth 10 points)
(08.01 HC)
Use the function f(x) to answer the questions:
f(x) = 5x²+2x-3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

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MrRoyal MrRoyal · Answer 1 · 2022-08-10T14:25:10+02:00

The vertex of the function is a minimum and the coordinate of the vertex of the function is (0.2, -2.4)

Part A: What are the x-intercepts of the graph of f(x)

The function is given as:

f(x) = 5x^2 + 2x - 3

Expand the function

f(x) = 5x^2 + 5x - 3x - 3

Factorize the function

f(x) = (5x - 3)(x + 1)

Set the function to 0

(5x - 3)(x + 1) = 0

Solve for x

x = 3/5 and x =-1

Hence, the x-intercept is 3/5 and -1

Is the vertex of the graph of f(x) going to be a maximum or a minimum?

The vertex of the function is a minimum.

This is so because the leading coefficient of the function is positive

What are the coordinates of the vertex?

Here, we have:

f(x) = 5x^2 + 2x - 3

Differentiate and set to 0

10x + 2 = 0

Solve for x

x = -0.2

Substitute x = -0.2 in f(x) = 5x^2 + 2x - 3

f(0.2) = 5(0.2)^2 + 2(0.2) - 3

Evaluate

f(0.2) = -2.4

Hence, the vertex of the function is (0.2, -2.4)

What are the steps you would use to graph f(x)?

To do this, we simply plot the x-intercept and the vertex.

And then connect the points

Read more about quadratic functions at:

https://brainly.com/question/23680118

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