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

Apr 6, 2016

(2, 4)

#### Explanation:

The equation $y = a {x}^{2} + b x + c$ can be modified to the standard form
${\left(x - \alpha\right)}^{2} = \pm 4 p \left(y - \beta\right)$, gviing vertex $\left(\alpha , \beta\right)$ and parameter p for the size of the parabola.
This way, the vertex of the parabola $y = a {x}^{2} + b x + c$ is $\left(- \frac{b}{2 a} , c - {b}^{2} / \left(4 a\right)\right)$. .
Here, $a = - 1 , b = 4 \mathmr{and} c = 0$.

Of course, direct manipulation for the standard form is easier.