1. Quadratic Functions
Chapter 5

2. 5.1 Introduction to Quadratic Functions
A quadratic function is any function that can be written in the form:
f(x) = ax2 + bx +c

3. Identify a, b, and c for the following quadratics:
f(x) = x2 + 3x +7 a = b = c =
f(x) = 3x2 + 4x – 12 a = b = c =
f(x) = -x2 – 2x a = b = c =
f(x) = 20 – 4x – 2x2 a = b = c =

4. The graph of a quadratic is a parabola.
There are 2 types:
Opens up
Opens down
Vertex
Axis of Symmetry
Vertex
Axis of Symmetry

5. Let’s take a look at the graphs of 1-4
Let’s take a look at the graphs of 1-4. State whether it opens up or down.
f(x) = x2 + 3x up or down?
f(x) = 3x2 + 4x – 12 up or down?
f(x) = -x2 – 2x up or down?
f(x) = 20 – 4x – 2x2 up or down?
What do the “up” ones have in common?
What do the “down” ones have in common?

6. Maximum and Minimum Values
if a > 0 the parabola opens up, and the y-coordinate of the vertex is the minimum value.
Ex. (1.) f(x) = x2 + 3x +7 a = 1 opens up
find the vertex
vertex: min.:
if a < 0 the parabola opens down, and the y-coordinate of the vertex is the maximum value.
Ex. (2.) f(x) = -x2 + 4x – 12 a = -1  opens down
vertex: max.:

7. 5.2 Intro to Solving Quadratic Functions
Solve x2 = 9 for x therefore x = 3 or x = -3 If x2 = a and a ≥ 0, then

8. Properties of Square Roots:
Product Property of Square Roots:
if a ≥ 0 and b ≥ 0 :
Quotient Property of Square Roots:

9. Practice Problems
Solve 4x = 253 and give exact solutions.

10. Practice Problems
Solve 9(x – 2)2 = 121

11. Pythagorean Theorem
If ∆ABC is a right triangle with the right angle, then a2 + b2 = c2 .
Leg
Hypotenuse

12. Practice Problems
Find the unknown length in each right triangle. Give answers to the nearest tenth.
x = 2.5
y = 5.1 z

13. Practice Problems
Find the unknown length in each right triangle. Give answers to the nearest tenth.
q = 4.0 p
r = 8.2