Question

The vertex of the parabola below is at the point (2, 4), and the point (3,6) is
on the parabola. What is the equation of the parabola?
10
(3,6)
(2,4)
-10
10
-10
O A. y=2(x-2)² +4
OB. x= 4(y-3)² +1
O C. y= 6(x-2)2 +4
OD. y=3(x-4)2 +2
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Answer 1

The equation of the parabola is y = 2(x - 2)^2 + 4

How to determine the parabola equation?

The given parameters are:

• Vertex, (h,k) = (2,4)
• Point (x,y) = (3,6)

A parabola is represented as:

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

Substitute (h,k) = (2,4)

y = a(x - 2)^2 + 4

Substitute (x,y) = (3,6)

6 = a(3 - 2)^2 + 4

Evaluate the difference

6 = a(1)^2 + 4

This gives

6 = a + 4

Subtract 4 from both sides

a = 2

Substitute a = 2 in y = a(x - 2)^2 + 4

y = 2(x - 2)^2 + 4

Hence, the equation of the parabola is y = 2(x - 2)^2 + 4

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