Question

The graph of y = -3x2- 2x - 5 has a:
A. Maximum
B. Minimum

Find the vertex of the graph of the following equation: y = x2 + 8x -12.
A. (4, -28)
B. (-4, -28)
C. (-4, 4)
D. (4, 4)

Answer 1

For A, plot it. If it has a n shaped curve it has a maximum, if it has a U curve it has a minimum. Yours has a maximum.

as for #2, you can use the formula \(\ \sf -(\dfrac{b}{2a}) \)

In \(\ \sf \Large y = x^2 + 8x - 12 \)

\(\ \sf \Large B \rightarrow 8 \)
\(\ \sf \Large A \rightarrow 1 \)

\(\ \sf \Large -(\dfrac{8}{2(1)}) = -\dfrac{8}{2} = -4\)

Now plug in \(\ \sf \color{green}{-4}\) into \(\ \sf \Large f(\color{green}{x}) = \color{green}{x}^2 + 8\color{green}{x} - 12 \) and that'll be your coordinates to the vertex.

Answer 2

The formula is actually \(\ \sf \color{green}{x} = -(\dfrac{b}{2a}) \)

Answer 3

\[F(-4)-4^{2}+8(-4)-12\] @tHe_FiZiCx99

Answer 4

What's that?

Answer 5

i pluged in -4 into the green spaces

Answer 6

Yeah I thought that might help :>

Yeah you're right now simplify it, don't forget the equal sign!

f(-4) = (-4)^2+ 8(-4) - 12

Answer 7

What did you get?

Answer 8

i got C @tHe_FiZiCx99

Answer 9

No no, what did you get when you plugged in -4 into the function?

Answer 10

f(-4) = (-4)^2+ 8(-4) - 12
-4x^2+16-12

Answer 11

@tHe_FiZiCx99

Answer 12

Um no xD

What is -4^2 ? Btw, I think what confused you is the x, -4 takes the x place because x IS -4

Answer 13

-4*-4=16

Answer 14

Yes, now what is 8(-4) = ?

Answer 15

32

Answer 16

Nope, negative sign!

Answer 17

-32

Answer 18

Yes, now: 16 - 32 - 12 = ?

Answer 19

-28

Answer 20

Yes!

Now the cool part in this, remember the formula \(\ \sf x = -(\dfrac{b}{2a}) \) ?

Well when you solve that it gives you x = -4, now when you plugged that into the function, you got -28

So the coordinates are (-4,-28), this is where the vertex is!

Answer 21

thanksso much for the help

Answer 22

You're welcome :>