QF - Graphing Quadratics in Vertex Form (Lesson)

Graphing Quadratics in Vertex Form

In your exploration assignment, you defined what a quadratic function in vertex form looks like:

f of x equals a times x minus h quantity squared plus k 

You also explored what a, h, and k can do to the shape of your parabola. The table below defines that in appropriate math terms.

f(x) = a(x - h)2 + k

a

h

k

|a|>1: vertical stretch

|a|<1: vertical compression

Shifts the parabola left or right, use the opposite sign!

Shifts the parabola up or down.

If a is negative, the parabola reflects over the x-axis and opens down.

Vertex: (h, k)

State the Transformations Practice

For each function below, state the transformations and vertex from the parent function.

  1. f(x) = 2(x + 3)2
  2. f(x) = -(x - 2)2 + 1
  3. f(x) = (2/3)(x - 4)2 - 3

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

Let's try graphing some quadratic functions in vertex form. Watch this video:

 

Graphing Quadratic Functions in Vertex Form

Try these problems. Find the vertex, axis of symmetry, y - intercept, x - intercepts, and graph it.

  1. f(x) = (x + 2)2 - 1
  2. f(x) = -2(x + 1)2 + 6
  3. f(x) = (x - 7)2 + 3

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

IMAGES CREATED BY GAVS