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Final exams
a parabola has its vertex at (2, -3) and its y-intercept at 5.

part a:
write an equation of the parabola in the form
y = a(x-h)^2+k

Answer :

MRROYALGO

The equation of the parabola is y = 5(x -2)^2 - 3

How to determine the equation of the parabola?

A parabola is represented as:

y = a(x -h)^2 + k

It has its vertex at (2,-3).

This means that

(h,k) = (2,-3)

So, we have:

y = a(x -2)^2 - 3

It has its y-intercept at 5.

This means that

(x,y) = (0,5)

So, we have:

5 = a(0 -2)^2 - 3

Evaluate

5 = 4a - 3

Add 3 to both sides

4a = 8

Divide both sides by 4

a = 2

Substitute a = 2 in y = a(x -2)^2 - 3

y = 5(x -2)^2 - 3

Hence, the equation of the parabola is y = 5(x -2)^2 - 3

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