# How do you find the vertex of y = 5x^2 + 4x - 3?

Jul 29, 2015

The vertex is at color(red)((-2/5,-19/5).

$y = 5 {x}^{2} + 4 x - 3$

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

$a = 5$, $b = 4$, and $c = - 3$.

The $x$-coordinate of the vertex is at x = -b/(2a) = -4/(2×5) = -4/10 = -2/5.

To find the $y$-coordinate of the vertex, we insert $x = - \frac{2}{5}$ into the equation.

$y = 5 {x}^{2} + 4 x - 3 = 5 {\left(- \frac{2}{5}\right)}^{2} + 4 \left(- \frac{2}{5}\right) - 3 = 5 \left(\frac{4}{25}\right) - \frac{8}{5} - 3$

$= \frac{20}{25} - \frac{8}{5} - 3 = \frac{4}{5} - \frac{8}{5} - \frac{15}{5} = - \frac{19}{5}$

The vertex is at ($- \frac{2}{5} , - \frac{19}{5}$).