This document discusses quadratic equations and functions. It explains that a quadratic equation is an equation of degree 2 that can be written in standard form as ax2 + bx + c = 0. It provides examples of quadratic equations and shows how to write equations in standard form. The document also discusses several methods for solving quadratic equations, including factoring, graphing, completing the square, and using the quadratic formula. It introduces the square root principle for solving equations of the form x2 = a.

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