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Topic: The Parabola. The Graph of a quadratic function is a curve whose shape is called a parabola. Example : f(x) = 3x 2. Points to Remember. The parabola generated by y = ax 2 + bx + c opens Upward if a > 0 Downward if a < 0. - PowerPoint PPT Presentation
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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?
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