To find the vertex, [tex](h,k)[/tex], or a quadratic of the form [tex]ax^2+bx+c[/tex], we are going to use the vertex formula: [tex]h= \frac{-b}{2a} [/tex], and then, we are going to evaluate the function at [tex]h[/tex] to find [tex]k[/tex]:
We can infer four our quadratic 4x^2+8x-8 that [tex]a=4[/tex] and [tex]b=8[/tex], so lets replace those values in our formula to find [tex]h[/tex]: [tex]h= \frac{-b}{2a} [/tex] [tex]h= \frac{-8}{(2)(4)} [/tex] [tex]h= \frac{-8}{8} [/tex] [tex]h=-1[/tex]
To find [tex]k[/tex] we are going to evaluate the quadratic at [tex]h=-1[/tex]. In other words, we are going to replace [tex]x[/tex] with -1: [tex]4x^2+8x-8[/tex] [tex]k=4(-1)^2+8(-1)-8[/tex] [tex]k=4-8-8[/tex] [tex]k=-12[/tex]
Our vertex is (-1,-12). We can conclude that the y value of the vertex of 4x^2+8x-8 is -12.