Quadratic Functions

Question

Use completing the square to write the following equations in vertex form. State the vertex and whether the parabola has a maximum or minimum value.

1) y = x^2 - 10x + 3

2) y= -x^2 + 12x +2

3) y = 4m^2 + 32m + 33

Answer 1

The vertex form of a parabola is y = a(x-h)² + k. The vertex is (h,k). If a > 0, the vertex is the lowest point on the graph. If a < 0, the vertex is the highest point on the graph.

y = 4m² + 32m + 33

y - 33 = 4(m² + 8m)

y - 33 = 4(m² + 8m + 16 - 16) [using completing the square]

y - 33 = 4(m + 4)² - 64

y = 4(m + 4)² - 31

The vertex is (-4,-31) and the vertex is the minimum point.

The other two problems can be done in a similar manner.