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If possible can someone please review my understanding of this question.

1. The problem statement, all variables and given/known data

At what point on the Parabola y= 2x^2-7x-15 will a normal to the parabola have a gradient of -1/2

2. Relevant equations

3. The attempt at a solution

We are given the gradient of the normal as -1/2

Therefore gradient of the tangent = 2

dy/dx = 4x - 7 = 2

4x = 9

x = 2.25 (2 1/4)

plug into y = 2(2.25)^2 - 7(2.25) - 15

y = -20 5/8

Therefore the point on the parabola - where a normal to the parabola will have a gradient of

-1/2 = (2 1/4, -20 5/8).

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# Homework Help: Normals to Curves (Differentiation)

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