# How do you find the standard form of the equation of the parabola with a vertex of (-1,4) and x intercepts of (-3,0) and (1,0)?

Nov 28, 2016

#### Explanation:

If the x intercepts are $\left(- 3 , 0\right) \mathmr{and} \left(1 , 0\right)$, then $\left(x + 3\right)$ and $\left(x - 1\right)$ are factors:

$y = k \left(x + 3\right) \left(x - 1\right)$

To find the value of k, substitute -1 for x and 4 for y:

$4 = k \left(- 1 + 3\right) \left(- 1 - 1\right)$

$4 = k \left(2\right) \left(- 2\right)$

$k = - 1$

$y = - 1 \left(x + 3\right) \left(x - 1\right)$

Use the F.O.I.L. method to multiply the binomials:

$y = - 1 \left({x}^{2} - x + 3 x - 3\right)$

$y = - 1 \left({x}^{2} + 2 x - 3\right)$

Distribute the -1:

$y = - {x}^{2} - 2 x + 3$

This is standard form.