Quadratic equations and function

1. Quadratic
Equations and
Function

2. In this chapter, you will learn to:
•Illustrate quadratic equations
•Solve quadratic equations by extracting
square roots and factoring.

3. Quadratic Equations
A quadratic equation in one variable is an
equation of degree 2. the standard form of a quadratic
is
𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎,
where a, b, and c are real numbers, and a ≠ 0

4. Quadratic Equations maybe written in various forms.
𝟑𝒙 𝟐 − 𝟐𝟑𝒙 = 𝟖
𝟐𝒙 𝟐 = 𝟗
𝟒𝒙 𝟐 = −𝟏𝟐𝒙

5. Working with a quadratic equation is usually simplified when
the quadratic is written in standard form, 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 = 𝟎
Write each quadratic equation in standard form and
determine a, b, and c.
1) 5𝑥2 + 3𝑥 = 8
2) 2𝑥2
= −8𝑥
3) 3𝑥 = 5𝑥2
4) 5 − 7𝑥 = 5𝑥2
Solution:

6. There are several ways to solve quadratic
equations.
1)Factoring
2)Graphing
3)Completing the square
4)Using the Quadratic Formula

7. Square Root Principle
If 𝒙 𝟐
= 𝒂 and 𝒂 ≥ 𝟎, then
𝒙 = 𝒂 or 𝒙 = − 𝒂
It is common to indicate the positive and negative
solutions by writing ± 𝒂, read as “plus and minus the
square root of a”
For example: if 𝒙 𝟐
= 𝟐𝟓, then 𝐱 = ± 𝟐𝟓 or ±𝟓

8. Solve for x.
Solution:1) 𝑥2
= 49
2) 𝑥2
+ 3 = 39
3) 4𝑥2
− 9 = 71
4) 5𝑥 − 3 𝑥2
= −32