An expression is shown below.

f(x) = 4x2 + 8x - 5

part a: what are the x-intercepts of the graph of f(x)? show your work.

part b: is the vertex of the graph of f(x) going to be a maximum or minimum? what are the coordinates of the vertex? justify your answers and show your work

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.

Part A) The x-intercepts are the points (-2.5,0) and (0.5,0)

Part B) The vertex is a minimum and the coordinates are (-1,-9)

Part C) see the explanation

Step-by-step explanation:

we have

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

we know that

The x-intercepts are the values of x when the value of the function f(x) is equal to zero

so

For f(x)=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

therefore

The x-intercepts are the points (-2.5,0) and (0.5,0)

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex?

we know that

The quadratic equation represent a vertical parabola open upward (because the leading coefficient is positive)

therefore

The vertex represent a minimum

Convert to vertex form

Factor 4

Complete the square

Rewrite as perfect squares

> equation in vertex form

The vertex is the point (-1,-9)

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

To graph f(x)

I need

1) The direction of the graph (Is a vertical parabola open upward)

2) The coordinates of the vertex (-1,-9) ( in this case is a minimum)

3) The x-intercepts  (-2.5,0) and (0.5,0)

4) The y-intercept

The y-intercept is the value of f(x) when the value of x is equal to zero

so

For x=0

The y-intercept is the point (0,-5)

Plot the points and draw the parabola

see the attached figure to better understand the problem

rounding to the nearest thousandth would be 452,000

what do you need me to answer?

step-by-step explanation: