# How do you find the vertex of a parabola y=(x+5)(x+3)?

Jul 19, 2015

The vertex is at color(red)((-4,-1).

#### Explanation:

$y = \left(x + 5\right) \left(x + 3\right)$

$y = {x}^{2} + 8 x + 15$

The standard form of the equation for a parabola is

$y = a {x}^{2} + b x + c$

By comparing the two equations, we see that

$a = 1$, $b = 8$, and $c = 15$.

The $x$-coordinate of the vertex is at x = -b/(2a) = -8/(2×1) = -8/2 = -4.

To find the $y$-coordinate of the vertex, we insert $x = - 4$ into the equation.

$y = \left(x + 5\right) \left(x + 3\right) = \left(- 4 + 5\right) \left(- 4 + 3\right) = 1 \left(- 1\right) = - 1$

The vertex is at ($- 4 , - 1$).