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

Question

1659 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-11T19:24:38

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

Currently your equation is in standard form:

$y = a x^{2} + b x + c$ $y=ax^2+bx+c$ where $(- \frac{b}{2 a}, f (- \frac{b}{2 a}))$ $(-b/(2a),f(-b/(2a)))$ is the vertex

We want to put it in vertex form:

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

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

$- \frac{b}{2 a} = - \frac{- 27}{2 (- 6)} = (\frac{27}{- 12}) = (- \frac{9}{4}) = - 2.25$ $-b/(2a)=-(-27)/(2(-6))=(27/-12)=(-9/4)=-2.25$

So:

$f (- 2.25) = - 6 {(- 2.25)}^{2} - 27 (- 2.25) - 18$ $f(-2.25)=-6(-2.25)^2-27(-2.25)-18$

$= - 30.375 - 60.75 - 18 = - 109.5$ $=-30.375-60.75-18=-109.5$

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

Thus our equation is:

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

What is the vertex form of y=−6x2−27x−18y= -6x^2 -27x-18?