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Exit Level

TAKS Preparation UnitObjective 5

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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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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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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

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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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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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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

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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

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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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