Question

A parabola has vertex (1, −2) and passes through the point (3, 2). Find its equation

Answer 1

Below in bold.

Explanation:

The general vertex form for a parabola is:

y = a(x - b)^2 + c where a is a constant, and (b, c) is the vertex.

So here we have b = 1 and c = -2 giving:

y = a(x - 1)^2 - 2

When x = 3, y = 2 , therefore:

2 = a(3-1)^2 - 2

4a = 2+2 = 4

a = 1

So our equation is

y = (x - 1)^2 - 2.

In standard form:

y = x^2 - 2x + 1 - 2

y = x^2 -2x - 1.