Question

What are the x-intercepts of the graph of f(x)?
f(x) = -16x2 + 24x + 16

Answer 1

f(x)=-16x^2 + 24x +16

Answer 2

The x intercepts are: -0.5 and 2

Answer 3

dont give out the answers you have to guide them

Answer 4

All you have to do is graph it.

https://www.desmos.com/calculator

Answer 5

−16 x 16+24x+16
−256+24x+16
−240+24x
24(−10)+24x
24(−10+x)

Answer 6

well you should have said that before

Answer 7

:P

Answer 8

@greenlegodude thanks for that resource

Answer 9

let me test it out to see how it works

Answer 10

It's an amazing resource, just copy & paste your equation in the box at the left, then look at the lines crossing the x-axis. Those will be the x-intercepts.

Answer 11

pretty cool
now how do i figure out this part
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.

Answer 12

same equation

Answer 13

The vertex is the top of the graph

Answer 14

0.75, 25

Answer 15

If A(-16 in the equation) is greater than 0 then it will be a minimum, but if A is less than 0, it will be a maximum. So is the graph a maximum or a minimum?

Answer 16

it will be a maximum in this case

Answer 17

Yes, good job.

Answer 18

Btw, to find the vertex use the equation: \[-\frac{ b }{ 2a }\]

Answer 19

Your equation is in the form of ax^2 + bx + c

Answer 20

So your points are:

\[a = -16\]
\[b = 24\]
\[c = 16\]

Answer 21

Plug them into the equation!

\[-\frac{ 24 }{ 2(-16) }\]
\[-\frac{ 24 }{ 32 }\]
\[0.75\]

Answer 22

That's the x value of the vertex.

Answer 23

You can plug in '0.75' for x in the equation and find out what 'y' is:

\[f(x) = -16x^2 + 24x + 16\]
\[f(x) = -16(0.75)^2 + 24(0.75) + 16\]
\[f(x) = -16(0.5625) + 18.75 + 16\]
\[f(x) = -9 + 18.75 + 16\]
\[f(x) = 9.75 + 16\]
\[f(x) = 25.75 \]

So the vertex is approximately (0.75, 25.75)

Answer 24

this is awesome thank you for such detailed explanation

Answer 25

No problem.