Math 103
Group Activity Problems (W9B)
Name:___________________________
Vertex Form of a Quadratic Function
Section 3.1 (Due June 1)
Prerequisite Skills
- Multiplying and dividing fractions
- Expanding binomials
- Factoring perfect squares
Key Terms
-
Learning Objectives for this Activity
Quadratic Function
Vertex of a quadratic function.
Vertex Form of a quadratic function.
Standard Form of a quadratic function.
Completing the square.
1. Identify the following: Is it a quadratic or not?
a.
b.
- Identify the vertex of a parabola from its formula in
vertex form.
- Convert quadratic equations/functions between
standard form and vertex form.
c.
d.
2. Identify the following: Is it a quadratic or not?
a. 𝑓(𝑥) = 10𝑥 − 3
b. 6 − 𝑥 2 + 𝑥 = 𝑦
c.
5𝑥 2
𝑥
= 𝑔(𝑥)
d. 7𝑥 2 𝑥 + 1 = 𝑎(𝑥)
e. 𝑐(𝑥) = 3 + 2𝑥 2
3. A quadratic function f is graphed
a.
Find the vertex. What is the coordinate point?
b. What is the domain of f?
What is the range of f?
c. Fill in the box
d. The x-value of the vertex is the h. The y-value of the vertex is the k.
Find the (x, y) coordinates of one other point on the graph. Plug all
those in and solve for a to finish your equation.
Vertex Form of a Quadratic
The formula for a quadratic function is in
vertex form if it is written as (see page 159):
If a quadratic function is in vertex form then
its vertex is at the point (see page 159):
4. We can convert standard form f (x) = ax 2 + bx + c to vertex form. This process is often called completing the
square. Note: In this course we will focus on completing the square when a = 1. In MTH 111, you will work on
completing the square when the a-value is any number.
a.
Convert g (t )  t 2  8t  3 to vertex form.
What is the vertex of g (t )  t 2  8t  3 ? WRITE AS A COORDINATE POINT.
b. Convert f ( x)  x 2  6 x  11 to vertex form.
c. CHECK YOUR WORK! Expand your result from step b.
d. Identify the vertex of f ( x)  x 2  6 x  11 .
The process of converting a
quadratic equation from
standard form to vertex
form is called completing
the square.