Question

Which is the vertex form of the equation for the quadratic function y = -x2 - 6x -7

Answer 1

The standard form of the quadratic function is ax^2+bx+c

the function here

$y=-x^2-6x-7$

is in this form, by comparison a= - 1, b= - 6 and c = -7

The vertex form is :

$y=a(x-h)^2+k$

where (h,k) are the coords of the vertex. the x-coord of the vertex

$h=\frac{-b}{2a}=-\frac{-6}{2(-1)}=-3$

and y-coord

$k=-(-3)^2-6(-3)-7=2$

here

$(h,k)=(-3,2)\text{ and a=-1}$$y=-(x+3)^2+2$

that is the equation