Algebra one question

Question

F(x)= ax^2+bc+c

vertex (0,2)

passes through (1,3)

Answer 1

The vertex form of a quadratic has the vertex built right into it, so let's use that form and then we can convert back to standard form.

The vertex form is:

f(x) = a(x - h)² + k where the vertex is the point (h, k)

Since the vertex is (0, 2), that gives us: f(x) = a(x - 0)² + 2 but we still are missing what the value of "a" is. To find that, we plug in the point that was given to us (1. 3) which is an (x, y). [x = 1 and y = 3]

So:

3 = a(1 - 0)² + 2

1 = a(1)²

a = 1

So f(x) = 1(x - 0)² + 2, or by simplifying, f(x) = x² + 2

This is already in standard form.