2. Objectives
1. define a quadratic equations;
2. write quadratic equation in standard form
ax² + bx + c = 0; and
3. identify the real numbers a, b, and c.
3. Activity 1: Do You Remember These Products?
Find each indicated product then answer the questions that follow.
1. 4(y² - 15) 2. (x + 5) (x – 5) 3. (2a – 3) ( a + 5)
4. (3x – 7) (3x – 7) 5. (6 – 5x)²
Questions:
a. How did you find each product?
b. In finding each product, what mathematics concepts or
principles did you apply?
4. Activity 2: Another Kind of Equation!
Below are different equations. List all linear equations and
quadratic equations.
𝑥2
− 6𝑥 − 7 = 0
3𝑥 + 5𝑦 = 8
9𝑎 + 5 = 23
𝑦2
+ 7𝑥 + 10 = 0
6𝑥 − 7 = 0
𝑥2
= 25
𝑡2
− 10𝑡 + 21 = 0
4𝑚 + 5𝑛 = 9
5. Quadratic Equation
A quadratic equation in one variable is a mathematical
sentence of degree 2 that can be written in the following
standard form.
Standard Form: 𝒂𝒙𝟐
+ 𝒃𝒙 + 𝒄 = 𝟎
where a, b, and c are real numbers and a ≠ 𝟎.
In the equation, 𝒂𝒙𝟐
is the quadratic term, bx is the linear
term, and c is the constant term.
6. A. If the given is quadratic equation, then find what is a, b,
and c.
Example 1.) 4𝑥2
+ 7𝑥 − 6 = 0
Example 2.) 5𝑥 3𝑥 + 2 = 25
Example 3.) (2x + 3) (x + 5)= -8
Example 4.)
2𝑥
3
+
5𝑥−3
𝑥
= 10
Example 5.) A flowerbed is to be 3m longer than its
width. The flowerbed will have an area of 70m².
7. Activity 3: Quadratic or not Quadratic
Identify which of the following equations are quadratic
and which are not. If the equation is not quadratic, explain.
1.) 3x + 10 = 15 5.) (a + 9)² = 0
2.) a² - 5a + 10 = 0
3.) (x – 4) (x + 5) = 14
4.) 6 – 3x + 4x² = 0
8. Activity 4: Set Me to Your Standard
Write each quadratic equation in standard form, 𝑎𝑥2
+
𝑏𝑥 + 𝑐 = 0 then identify the values of a, b, and c.
1.) 3x – 2x² = 9 4.) (x + 5) (x – 5) = -3x
2.) (x + 4) (x – 5) = 0 5.) (x + 2)² = 4(x – 8)
3.) 2x(x – 5) = 15
