taylorlydell4
Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

(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)

Sagot :

MrRoyal

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

#SPJ1

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.