# What is the vertex form of y=4x^2-32x+63?

Jan 15, 2016

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

#### Explanation:

If the standard form of a quadratic equation is -

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

Its vertex form is -

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

$a =$co-efficient of $x$
$h = \frac{- b}{2 a}$
$k = a {h}^{2} + b h + c$

Use the formula to change it to vertex form -

$y = 4 {x}^{2} - 32 x + 63$
$a = 4$
$h = \frac{- \left(- 32\right)}{2 \times 4} = \frac{32}{8} = 4$
$k = 4 {\left(4\right)}^{2} - 32 \left(4\right) + 63$
$k = 64 - 128 + 63$
$k = 127 - 128 = - 1$

Substitute a=4; h=4 : k=-1 in

$y = a {\left(x - h\right)}^{2} + k$
$y = 4 {\left(x - 4\right)}^{2} - 1$