# How do you write the equation of each parabola in vertex form given vertex at (0,4) and passes through the point (-1,6)?

Feb 27, 2016

$y = 2 {x}^{2} + 4$

#### Explanation:

$y = a {\left(x - h\right)}^{2} + k$ => equation of the parabola in vertex form where:
(h, k) is the coordinates of the vertex.
So in this case we substitute the given coordinates in the formula:
$y = a {\left(x - 0\right)}^{2} + 4$ => simplify:
$y = a {x}^{2} + 4$ => to solve for a we substitute the given coordinates:
$6 = a \cdot {\left(- 1\right)}^{2} + 4$ => simplify:
$6 = a + 4$ => solve for a
$6 - 4 = a$ => or:
$a = 2$ => substitute for a and the required equation is:
$y = 2 {x}^{2} + 4$