Topic: The Parabola.

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Presentation transcript:

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: x ( x + 3 ) = 0 Ans. x = 0 and x = -3 (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. Express the quadratic equation in the standard form ax2 + bx + c = 0. Factor ax2 + bx + c as a product of linear factors. Equate each linear factor to zero. Solve each resulting equation.

Examples 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

3x( x – 7 ) = 0 Factor the left side 3x = 0 and x – 7 = 0 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-Share Solve 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?