Question

I WILL MEDAL!!
An expression is shown below:
f(x) = -16x2 + 24x + 16

Part A: What are the x-intercepts of the graph of f(x)? Show your work.

Answer 1

We will need to set it equal to a number

If the X intercept is the point where it crosses the X axis, what does y always equal at that point

Answer 2

so far i have this -16x^2+24x+16
-8(2x^2-3x-2)=0

Answer 3

That's a good factor! You found out one of the X intercepts, do you see it?

Answer 4

Right. In other words, you've set y = to 0. Can you now solve the resulting equation?

Answer 5

In other words, factor (2x^2-3x-2).

Answer 6

so would one of them be (8,0) because -8 + 8 equals 0 right?

Answer 7

Not exactly, because its a constant factored out, you don't need to bring it over to the other side

Answer 8

In effect, you're saying that if you substitute x=8 into the original equation, you'd get zero for your answer. Why ot check that?

Answer 9

In other words, does f(x) = -16x2 + 24x + 16 = 0 if x = 8?

Answer 10

I think I have it would it be 2x^2-4x+x-2
2x(x-2) 1(x-2)
(x-2) (2x+1)
therefore the 0's are 2 and -1?

Answer 11

To help you answer your question: does f(x) = -16x2 + 24x + 16 = 0 if x = 2?

Answer 12

yes it would equal 0

Answer 13

then x=2 is a zero!
You can test whether x=-1 is or is not a zero.
8 is NOT a zero.

Answer 14

How many horiz. intercepts has this function? What are they? Express them as points, please.

Answer 15

two i think would it be (-0.25 , 0) and (0.75 , 0)

Answer 16

How did you get .75 and -.25 if I may ask?

Answer 17

Actually, you've already found the x-coordinates of the horiz. intercepts: {-1,2}.
One such intercept is therefore (-1,0). What is the other?

Answer 18

wait so would it be (-.5,0) too

Answer 19

Emmy, you have already found the zeros of the given function. They are x=-1 and x=2.
These are ALSO the x-coordinates of your horiz. intercepts, which are (-1,0) and (2,0).
that's it. No further work is necessary. Unfortunately, 9-.5,0) is incorrect.