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Andy completes the square for the equation x2 + 6x - 8 = 0. Which of the following equations reveals the vertex of the parabola? will fan and medal

Verified Answer :

Hagrid

If the equation \(x^2+6x-8\) has undergo completing the square, the answer would be:
\(x^2+6x-8\)
\(x^2+6x+9-8-9\)
**In this example, since 6x is the middle term, what comes to my mind is the polynomial (x+3) because 2ab results into 6x. [from the special products lesson \((a+b)^2=a^2+2ab+b^2\) ] 
\((x+3)^2 -17 = 0\)
So if the equation is equal to y, then this equation's
\(y+17=(x+3)^2\)
The vertex would be on the point (-3, -17)

botellok

Answer:

(h,k) in the cuadratic formula y= a(x-h)^2 + k

Step-by-step explanation:

If you complete square in a cuadratic formula the vertex of the parabola will be more visible. In the case of f(x)= \(x^{2}+6x-8\) we complete square adding and substracting 9. So,

\(x^{2}+6x+9-9-8 = (x+3)^{2}-17\)

So we have the cuadratic form of a parabola \(y= a(x-h)^{2} + k\) where a=1, h= -3 and k= -17.

So, the vertex is (h,k)=(-3,-17).

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