Answer:
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
