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

Feb 21, 2018

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

Explanation:

Vertex form is given by:

$y = a {\left(x - h\right)}^{2} + k$ with $\left(h , k\right)$ as the vertex.

Plug in the vertex.

$y = a {\left(x + 3\right)}^{2} - 32$

Plug in the point:

$- 14 = a {\left(0 + 3\right)}^{2} - 32$

$- 14 = 9 a - 32$

$9 a = 18$

$a = 2$

The vertex form is:

$y = 2 {\left(x + 3\right)}^{2} - 32$

Expand:

$y = 2 \left({x}^{2} + 6 x + 9\right) - 32$

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

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