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=(-b)/(2a)=-(-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