# Question #c85cb

Nov 22, 2016

$y = - 2 {\left(x - 4\right)}^{2} + 3$

#### Explanation:

$y = a {\left(x - p\right)}^{2} + q$ is the vertex form of a quadratic equation with vertex $\left(p , q\right)$ As we are given the vertex as $\left(4 , 3\right)$, we have $\left(p , q\right) = \left(4 , 3\right)$. Substituting these in, we can write the equation as

$y = a {\left(x - 4\right)}^{2} + 3$

As the graph passes through the point $\left(1 , - 15\right)$, we have

$- 15 = a {\left(1 - 4\right)}^{2} + 3$

$\implies - 15 = a {\left(- 3\right)}^{2} + 3$

$\implies - 15 = 9 a + 3$

$\implies - 18 = 9 a$

$\therefore a = - 2$

Thus the vertex form of the given quadratic is

$y = - 2 {\left(x - 4\right)}^{2} + 3$