The document outlines the definition and characteristics of quadratic equations, emphasizing their degree of 2 and standard form. It provides examples of real-life situations that illustrate the application of quadratic equations, such as building design, product demand, and projectile motion. Additionally, it includes practice exercises for identifying quadratic equations and assignments related to real-life scenarios.

1. Good Morning
MATHEMATICS 9 July 30, 2024

2. PRAYER

3. OBJECTIVES
Define quadratic equation.
Identify whether the given equation is a quadratic or not.
Illustrate quadratic equation in real life situation.

4. DEFINITION OF TERMS
Quadratic Equation
A quadratic equation in one variable is a mathematical sentence
of a degree of 2 that can be written in standard form.

5. It is a quadratic equation in standard form with a = 2,
b = 5, and c = -3.
EXAMPLE #1

6. It is a quadratic equation. However, it is not written in
standard form.
See on the board how it becomes a quadratic equation.
EXAMPLE #2

7. It is a quadratic equation. However, it is not written in
standard form.
See on the board how it becomes a quadratic equation.
EXAMPLE #3

8. When b = 0 in the equation ax2
+ bx + c = 0, it results to
a quadratic equation of the form ax2
+ c = 0.
EXAMPLES

9. Real life examples that illustrate quadratic equation
A rectangular building is to be placed on a lot
that measures 30m by 40m. The building must
be placed in the lot so that the width of the
lawn is the same on all four sides of the building.
Local restrictions state that the building cannot
occupy any more than 50% of the property.

10. Real life examples that illustrate quadratic equation
A manufacturer develops a formula to
determine the demand for its product
depending on the price in dollars. The formula is
D = 2,000 + 100P - 6P2
where P is the price per unit, and D is the
number of units in demand.

11. Real life examples that illustrate quadratic equation
A motorboat whose speed is 18
km/h in still water takes 1 hour
more to go 24 km upstream than to
return downstream to the same
spot.

12. Real life examples that illustrate quadratic equation
A ball is thrown upwards, 80m above the
ground. It will reach a maximum vertical
height and then fall back to the ground. The
height of the ball from the ground at time t
is h, and is given by h = -16t2
+ 64t + 80

13. SUM IT UP
Quadratic equations are used in many real-life
situations such as calculating the areas of an enclosed
space, the speed of an object, the profit and loss of a
product, or curving a piece of equipment for designing,
the parabolic trajectory, etc.
𝜽

14. PRACTICE EXERCISES
Identify if the given equation is quadratic or not. Copy and
answer.

15. ASSIGNMENT
Identify if the given situation illustrate quadratic equations. Write
Quadratic if it is otherwise Not Quadratic.