# How do you write standard form of quadratic equation of vertex (2,3) and yint = 11?

Feb 4, 2017

Write the equation in vertex form and then simplify to get standard form.

$y = 2 {x}^{2} - 8 x + 11$

#### Explanation:

Write in vertex form
$y = a {\left(x - h\right)}^{2} + k$
$y = a {\left(x - 2\right)}^{2} + 3$

Use y intercept to find constant $a$:
$11 = a \cdot 4 + 3$
$a = 2$

Rewrite and simplify with $a = 2$:

$y = 2 {\left(x - 2\right)}^{2} + 3$
$y = 2 \cdot \left({x}^{2} - 4 x + 4\right) + 3$
$y = 2 {x}^{2} - 8 x + 11$