What is the the vertex of y =-4x^2+2x+1 ?

Jan 4, 2016

$\left(\frac{1}{4} , \frac{5}{4}\right)$

Explanation:

The vertex form of a quadratic equation is
$y = a {\left(x - h\right)}^{2} + k$

where $\left(h , k\right)$ is the vertex of the quadratic.

To put the equation into vertex form, we can use a process called completing the square.

$y = - 4 {x}^{2} + 2 x + 1$

$= - 4 \left({x}^{2} - \frac{1}{2} x\right) + 1$

$= - 4 \left({x}^{2} - \frac{1}{2} x + \frac{1}{16} - \frac{1}{16}\right) + 1$

$= - 4 \left({x}^{2} - \frac{1}{2} x + \frac{1}{16}\right) + \frac{1}{4} + 1$

$= 4 {\left(x - \frac{1}{4}\right)}^{2} + \frac{5}{4}$

Thus the vertex is $\left(\frac{1}{4} , \frac{5}{4}\right)$