# What is the equation of the line normal to # f(x)=(2x-2)^2+4x# at # x=-3#?

##### 2 Answers

#### Explanation:

At

This is the gradient of the tangent.

So the gradient of the normal is

Equation of normal 0f #(-3,52) :

#### Explanation:

“Normal” means perpendicular to the line, or that the slopes will be opposite.

First we need to find the tangent line, which is the first derivative of the expression at x = -3.

https://www.symbolab.com/solver/tangent-line-calculator

Step-by-step solution here (long):

https://www.symbolab.com/solver/tangent-line-calculator/tangent%20of%20f%5Cleft(x%5Cright)%3D%5Cleft(2x%E2%88%922%5Cright)%5E%7B2%7D%2B4x%2C%20at%20x%3D%E2%88%923

THEN we need to find the equation of a line perpendicular to this one (inverse slope) passing through

The final line equation is thus: