© a very good teacher 2007 exit level taks preparation unit objective 5
TRANSCRIPT
© A Very Good Teacher 2007
Exit Level
TAKS Preparation UnitObjective 5
© A Very Good Teacher 2007
Quadratic Transformations
• The basic function y = ax² + c has two basic transformations.
• Changes to a make the graph wider or narrower
• Changes to c make the graph shift vertically (up or down)
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© A Very Good Teacher 2007
Quadratic Transformations, cont…• In the quadratic parent function a = 1
y = x² or y = 1x²
Decreasing a to a fraction less than 1, (but still positive) makes the graph wider.
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© A Very Good Teacher 2007
Quadratic Transformations, cont…
• Increasing a to a number greater than 1 makes the graph narrower.
• If a is a negative number, the graph opens down
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Quadratic Transformations, cont…
• Effects on c
• Increasing c shifts the graph up
• Decreasing c shifts the graph down
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Interpreting Quadratic Graphs• Pay attention to the
labels on the x- and y-axes
• Read the question carefully
• Example: How much time elapses while the rocket is 600 feet above the ground?
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4 seconds
© A Very Good Teacher 2007
Solving Quadratic Equations• The solutions, roots, or zeros of a
quadratic equation are the points where the parabola crosses the x-axis
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Solving Quadratic Equations, cont…
• You can solve a quadratic equation by graphing or factoring
• To solve by graphing, the equation must be in y = ax² + bx + c form.
• Then just graph it in the calculator and see where the parabola crosses the x-axis
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© A Very Good Teacher 2007
Solving Quadratic Equations, cont…
• Example: What are the roots of the quadratic equation x² - x – 6 = 0?
x = -2 x = 3
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© A Very Good Teacher 2007
Simplifying Polynomial Expressions• Rules of Exponents
• When adding and subtracting polynomials, exponents do not change
• When multiplying polynomials, add exponents
• When dividing polynomials, subtract exponents
• When raising a power to a power, multiply exponents
• Negative exponents switch places (top to bottom, or bottom to top)
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2 2 22 5 7a b a b a b
4 3 7a a a 5
32
aa
a
33 9a a
3 2 2 4
4 3
a b b c
c a
© A Very Good Teacher 2007
Simplifying Polynomial Expressions, cont…
• If you forget the rules… write it out the long way!
• Example: What is the simplified form of
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4 2 2 3
5
( 7 )(2 )
21
x y x y
x y
7 2
3 7
x x x x y y x x y y y
x x x x x y
What’s left?2
3
x y y y y 42
3
xy
© A Very Good Teacher 2007
Polynomial Expressions in word problems
• Determine the formula needed (usually area)
• Plug in the polynomials and simplify
• Example: What expression describes the area of a rectangle with width 5x²y³ and a length of 12xy²?
Area of a rectangle = length • width
Area = (12xy²) • (5x²y³)
Area = 3 560x y
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