Question

My math teacher and I can't figure this problem out please explain steps.

Determine the vertex of the given equation.
y = -3x2 - 8x - 4

Answer 1

When using the quadratic formula, the x-coordinate of the vertex of a parabola can be found from \[\frac{-b}{2a}\]

So in your case, the equation looks like:
\[-3x^{2}-8x-4\]

What do a and b equal?

Answer 2

a= -3
b= -8
c= -4

Answer 3

Correct! So if you plug your a and b into -b/2a, you get the x-coordinate of the vertex :)

Can you think of how you'd find the y-coordinate?

Answer 4

Yes and we came up with -4/3 for x coordinate now we just can't figure out how to get the y

Answer 5

Oh! Well, you have your equation
\[y = -3x^{2} - 8x -4 \]

And now, you have a value for x! So all you have to do is plug it into the equation to solve for y

Answer 6

we came up with 12 which isn't an option. We guessed 4/3 for the y answer

Answer 7

Ah, 4/3 is the correct answer. I think you guys may have dropped the negative in front of the 3?

Answer 8

\[-3 ( -\frac{4}{3})^{2} - 8 (-\frac{4}{3}) - 4\]
\[= -3 (\frac{16}{9}) + \frac{32}{3} - \frac{12}{3}\]
\[= -\frac{16}{3} + \frac{32}{3} - \frac{12}{3}\]
\[= \frac{4}{3}\]