Quadratic equation

2. Quadratic Equation
Factoring and
Completing the
Square

3. • A quadratic equation is an
algebraic equation of the
second degree in x.
• The quadratic equation in its standard
form is ax2 + bx + c = 0, where a and
b are the coefficients, x is the variable,
and c is the constant term.

4. ax2 + bx + c = 0

5. Example 1

6. Example 1

7. Example 1

8. Example 1

10. Solving Quadratic
Equations by
Factoring

11. Step 1 :
Transform the
quadratic equation
in standard form
Step 2 :
Factor the
polynomial
side of the
equation.

12. Step 3 :
Use the Zero-
Product Property
to equate factor to
zero
Step 4 :
Solve the resulting
equations

13. Step 5 : Check if
the obtained roots
are accurate by
substituting them
to the original
equation.

14. 𝒙𝟐
= 𝟔𝒙 + 𝟐𝟕

15. 5(𝒚𝟐
+ 𝟕)=-3(5y-8)+2y+17

16. In triangle inequality theorems, what is the
relationship between the lengths of the sides
of a triangle and its angles;
a. Hinge Theorem or SAS Inequality
Theorem

17. In triangle inequality theorems, what is the
relationship between the lengths of the
sides of a triangle and its angles;
b. Converse of Hinge Theorem or SSS
Inequality Theorem

18. If the lengths of the two sides of a
triangle is already given, how do we
get the range of the possible values
of the third side?

19. Lets Try!
If 𝑚∠𝑆 = 100˚ of 𝛥RST and
𝑚∠𝑊 = 80˚ of 𝛥JUL, which is
longer 𝑅𝑇 or 𝑉𝑋?
What is the opposite side of ∠S?
𝑹𝑻
Therefore, 𝑹𝑻 > 𝑽𝑿
What is the opposite side of ∠W?
𝑽𝑿
Since, m∠S > m∠W…

20. Lets Try!
If 𝐵𝐶 = 8 and 𝐸𝐹 = 7, which is
the larger angle, ∠A or ∠D?
Why?
What is the opposite angle of 𝐵𝐶 ?
∠A
Therefore,
𝒎∠𝑨 > 𝒎∠𝑫
Since 𝐵𝐶 > 𝐸𝐹 …
What is the opposite angle of 𝐸𝐹 ?
∠D

21. Solve for the possible length of
third side of a triangle

22. Activity

23. Assignment

24. “MISTAKES
are PROOF that you are
TRYING”