Question

Find the equation of the normal line to the parabola y=x^2-5x+4

Answer 1

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Answer 2

The normal is:

y=13(x−1)

Explanation:

The general equation of the normal line is:

y(ξ)−f(x)=−1f'(x)(ξ−x)

If we put the equation of the line in the same form:

y=13(x−5)

we can see the two lines are parallel when

−1f'(x)=13

f'(x)=−3

Take the derivative of f(x):

f'(x)=2x−5

and fond the value of x for which f'(x)=−3

2x−5=−3

x=1

The desired normal line is:

y−f(1)=−1f'(1)(x−1)

y=13(x−1)

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