Topic: The Parabola

The Graph of a quadratic function is a curve whose shape is called a parabola.

Example : f(x) = 3x2

Points to Remember

The parabola generated by

y = ax2 + bx + c opens

Upward if a > 0

Downward if a < 0

Topic: Solving Quadratic

Equations by Extracting the Square Root.

Key Concepts

Examples

Try this!

x2 = 49

Try this!

2x2 – 18 = 0

Try this!

Topic: Solving Quadratic

Equations by Factoring.

Key Concepts.

Zero Product Property

For any real numbers x and y, if

xy = 0, then either x = 0 or y = 0 or both are equal to zero.

Examples:

1.x ( x + 3 ) = 0 Ans. x = 0 and x = -3

2.(x-5) (x+3) = 0 Ans. x = 5 and x = -3

2. Procedures in Solving Quadratic Equation by Factoring.

a.

Procedures in solving quadratic equations by Factoring.

1. Express the quadratic equation in the standard form ax2 + bx + c = 0.

2. Factor ax2 + bx + c as a product of linear factors.

3. Equate each linear factor to zero.

4. Solve each resulting equation.

Examples

1. Solve x2 + 5x + 6 = 0

Solution:

x2 + 5x + 6 = 0 Write in S.F

(x+2) (x+3)= 0 Factor the left side

x + 2 = 0 and x+3 = 0 Set each factor

equal to zero

Answer: The solutions are -3 and -2

2. Find the roots of 3x2 – 21x = 0

Solution:

3x2 – 21x = 0 Write in S.F

3x( x – 7 ) = 0 Factor the left side

3x = 0 and x – 7 = 0

Therefore the roots are:

0 and 7

Try this!

x2 + 2x – 35 = 0

Try this!

x2 = x + 20

Try this!

3x2 + x = 0

Think-Pair-ShareSolve the following quadratic equations.

1. 7x2 – 28x = 0

2. 2b2 – 128 = 0

3. x2 = 196

4. y2 – 5y – 14 = 0

5. 3x2 + 2 = -7x

Board Drill

Solve the following quadratic equations.

x2 = 25

Board Drill

Solve the following quadratic equations.

x2 – 64 = 0

Board Drill

x2 – 16 = 0

Board Drill

4x2 = 49

Board Drill

3x2 = 48

Board Drill

8x2 + x = 0

Board Drill

7x2 + 21x = 0

Board Drill

5x2 – x = 0

Board Drill

16x2 + 8x = 0

Board Drill

3x2 + 15x = 0

Board Drill

x2 – 6x + 8 = 0

Board Drill

x2 + 7x + 6 = 0

Board Drill

x2 – 5x + 6 = 0

Board Drill

x2 + 9x + 14 = 0

Board Drill

x2 – 8x + 15 = 0

Board Drill

x2 + 3x = 10

Board Drill

x2 = 7x + 18

Board Drill

4x2 + 4x + 1 = 0

Board Drill

14x2 + 17x + 5 = 0

Homework

Answer the problem.

A vegetable garden measuring 30 feet by 20 feet has a walkway of uniform width around it. If the combined area of the garden and the walkway is 704 square feet; what is the width of the walkway?