Lesson 1
Introduction to
Quadratic Equations
Objectives
At the end of this lesson, the learner should be able to
● appropriately define and illustrate a quadratic
equation;
● correctly transform a quadratic equation to its
standard form; and
● accurately solve problems involving quadratic
equations.
Essential Questions
● What are the properties of quadratic equations?
● How is quadratic equation different from linear
equation?
● How will you transform a quadratic equation to its
standard form?
Warm Up!
Before we start studying quadratic equations, let’s have a
quick look on its history and possible applications by
watching the following video.
(Click on the link to access the video.)
“Quadratic Equations by Shmoop”. Shmoop.
Retrieved 24 January 2019 from
https://www.youtube.com/watch?v=fHH1FF9RWY0
Guide Questions
● How are quadratic equations different from linear
equations?
● What are some of the possible applications of quadratic
equations?
● What is the degree of a quadratic expression and how
does it affect the number of solutions of a quadratic
equation?
Learn about It!
1
Quadratic Equation
a second-degree polynomial equation that can be written in the standard form
ax 2  bx  c  0
where 𝑎, 𝑏, and 𝑐 are real numbers and 𝑎 ≠ 0
Example:
3𝑥 2 + 4𝑥 + 15 = 0 is a quadratic equation in standard form
where 𝑎 = 3, 𝑏 = 4, and 𝑐 = 1.
Try It!
Example 1: Determine whether the equation
4𝑥 − 2 = −4𝑥 2 − 5
is a quadratic equation or not.
Try It!
Example 1: Determine whether the equation
4𝑥 − 2 = −4𝑥 2 − 5
is a quadratic equation or not.
Solution: Write the equation in standard form.
Recall that the standard form of a quadratic equation is
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0.
Try It!
4 x  2  4 x  5
2
4x2  4x  2  5  0
4x  4x  3  0
2
The equation follows the standard form of a quadratic
equation where 𝑎 = 4, 𝑏 = 4, and 𝑐 = 3.
Try It!
Example 2: Write the quadratic equation 5𝑥 2 − 6𝑥 = 7𝑥 + 3𝑥 2
in standard form.
Try It!
Example 2: Write the quadratic equation 5𝑥 2 − 6𝑥 = 7𝑥
+ 3𝑥 2 in standard form.
Solution: The standard form of a quadratic equation is
2
ax  bx  c  0
1. Transpose all the terms to one side of the equation.
5 x  6 x  7 x  3x
2
5 x  3x  6 x  7 x  0
2
2
2
Try It!
2. Combine similar terms.
5 x 2  3x 2  6 x  7 x  0
2 x  13 x  0
2
3. Arrange the terms following the standard form of
quadratic equation.
The equation is already arranged in standard form where
𝑎 = 2, 𝑏 = −13, and 𝑐 = 0.
Let’s Practice!
Individual Practice:
1. Write your own example of a quadratic equation in
standard form. Determine the values of 𝑎, 𝑏, and 𝑐.
2. Write each equation in standard form.
a. 6 x  9 x  5
2
b. 10  5 x  2 x
c. 3 x  10 x
2
2
Let’s Practice!
Group Practice: To be done in groups of five.
The length of a rectangle is one less than twice its width. The
area of the rectangle is 45 square units.
Translate the above mathematical sentence into a
mathematical equation and write the equation in standard
form.
Key Points
1
Quadratic Equation
a second-degree polynomial equation that can be written in the standard form
ax 2  bx  c  0
where 𝑎, 𝑏, and 𝑐 are real numbers and 𝑎 ≠ 0
Synthesis
● How do we write a quadratic equation in its standard
form?
● How can you apply the concept of quadratic equation in
your daily life as a student?
● How will you determine whether a certain value is a
solution of a quadratic equation?