What is the vertex of the parabola given by the equation y = 9(x + 4)^2 – 3?

Question

anonymous · Answer

the base equation is y=a(x-h)^2 + k

vertex of parabola is as (h,k)

what is your vertex of parabola? (:

anonymous · Answer

would it be (-4, -3)? since the formula has a negative, you have to negate it right?

whpalmer4 · Answer

If you have the parabola in form $$y = ax^2+bx+c$$

which in this case would be $$y = 9x^2 +72x + 141$$the x-value of the vertex is given by $$x = -\frac{b}{2a} = -\frac{72}{2*9} = $$
The y-value you find by substituting that value of $x$ into the equation.

whpalmer4 · Answer

yes, that is correct.

anonymous · Answer

ah the negative. there's a foolproof way of finding out:
0=a(x-h)^2

make x your guessed answer, which is -4:
2((-4)+4)^2=?

if you get zero, then its your answer.
if you don't just try the opposite ^^

whpalmer4 · Answer

Here's a possibly slightly easier to understand way to find out: plug the point into the equation.  Does it work?  The vertex, after all, is a point on the parabola.  Let's say we guessed wrong, and said (4,-3):

$$y = 9(x+4)^2-3$$$$-3=9(4+4)^2-3$$$$-3=9(64)-3$$Uh, that's clearly not the right one.


$$-3 = 9(-4+4)^2-3$$$$-3=9(0)-3$$Now we're talking...

anonymous · Answer

((-4)+4)^2=0

works too
actually you don't even have to add the a or 9 :D

anonymous · Answer

Auxuris, thank you for giving me formulas to find the vertex with. Whpalmer4, thank you for explaining an easy way to see if the point fits. Thank you both so much! This helped me alot! I really wish I could give both of you a medal :(