# What is the vertex form of a parabola given vertex (41,71) & zeros (0,0) (82,0)?

Mar 1, 2016

The vertex form would be $- \frac{71}{1681} {\left(x - 41\right)}^{2} + 71$

#### Explanation:

The equation for vertex form is given by:
$f \left(x\right) = a {\left(x - h\right)}^{2} + k$ , where the vertex is located at point $\left(h , k\right)$

So,substituting the vertex $\left(41 , 71\right)$ at $\left(0 , 0\right)$,we get,

$f \left(x\right) = a {\left(x - h\right)}^{2} + k$

$0 = a {\left(0 - 41\right)}^{2} + 71$

$0 = a {\left(- 41\right)}^{2} + 71$

$0 = 1681 a + 71$

$a = - \frac{71}{1681}$

So the vertex form would be
$f \left(x\right) = - \frac{71}{1681} {\left(x - 41\right)}^{2} + 71$.