What is the vertex form of y= -6x^2 -27x-18?

1 Answer
Oct 11, 2017

y=-6(x+2.25)^2-109.5

Explanation:

Currently your equation is in standard form:

y=ax^2+bx+c where (-b/(2a),f(-b/(2a))) is the vertex

We want to put it in vertex form:

y=a(x-h)^2+k where (h,k) is the vertex

We know a=-6, but we have to figure out the vertex to find h and k

-b/(2a)=-(-27)/(2(-6))=(27/-12)=(-9/4)=-2.25

So:

f(-2.25)=-6(-2.25)^2-27(-2.25)-18

=-30.375-60.75-18=-109.5

Thus our vertex is (-2.25, -109.5) and h=-2.25, k=-109.5

Thus our equation is:

y=-6(x+2.25)^2-109.5