An expression is shown below:

f(x) = −8x2 + 30x + 8

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

part b: is the vertex of the graph of f(x) going to be a maximum or minimum? justify your answer

part c: what is the y intercept of the graph?

Part A. the x-intercepts are: x=4 and x= -1/4

Part B. The vertex of the graph is going to be a maximum

Part C. y-intercept is y=8

Step-by-step explanation:

We have the following function:

f(x) = −8x^2 + 30x + 8

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

To find the x-intercepts we have to make y=0 and solve for x. Then:

y = −8x^2 + 30x + 8

0 = −8x^2 + 30x + 8

8x^2 - 30x - 8  = 0

Dividing the whole expression by 8:

x^2 - 15/4x - 1  = 0

Using the quadratic formula we have that:

(x−4)(4x+1)

So the x-intercepts are: x=4 and x= -1/4

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

The vertex of the graph is going to be a maximum, given that the quadratic term is multiplied by a negative sign.

PArt C. What is the y intercept of the graph?

To calculate the y-intercept we need to make x=0, so:

y = −8(0)^2 + 30(0) + 8 = 8

So the y-intercept is y=8