# What is the vertex form of y=x^2+14x+3 ?

${\left(x + 7\right)}^{2} = y + 46$

#### Explanation:

Given equation:

$y = {x}^{2} + 14 x + 3$

$y = {x}^{2} + 2 \left(7\right) x + {7}^{2} - {7}^{2} + 3$

$y = {\left(x + 7\right)}^{2} - 46$

${\left(x + 7\right)}^{2} = y + 46$

The above equation is in vertex form of upward parabola: ${\left(x - {x}_{1}\right)}^{2} = 4 a \left(y - {y}_{1}\right)$

The vertex of parabola :$\left(x - {x}_{1} = 0 , y - {y}_{1} = 0\right)$

$\left(x + 7 = 0 , y + 46 = 0\right) \setminus \equiv \left(- 7 , - 46\right)$

Jul 22, 2018

$y = {\left(x + 7\right)}^{2} - 46$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

•color(white)(x)y=a(x-h)^2+k

$\text{where "(h,k)" are the coordinates of the vertex and a}$
$\text{is a multiplier}$

$\text{to obtain this form "color(blue)"complete the square}$

$y = {x}^{2} + 2 \left(7\right) x + 49 - 49 + 3$

$y = {\left(x + 7\right)}^{2} - 46 \leftarrow \textcolor{red}{\text{in vertex form}}$