Write the equation in standard form for the quadratic equation whose vertex is at (-3,-32) and passes through the point (0,-14) ?

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Answer 1 · 2018-02-21T17:19:48

$y=2x^2+12x-14$

Vertex form is given by:

$y=a(x-h)^2+k$ with $(h,k)$ as the vertex.

Plug in the vertex.

$y=a(x+3)^2-32$

Plug in the point:

$-14=a(0+3)^2-32$

$-14=9a-32$

$9a=18$

$a=2$

The vertex form is:

$y=2(x+3)^2-32$

Expand:

$y=2(x^2+6x+9)-32$

$y=2x^2+12x+18-32$

$y=2x^2+12x-14$