1. © A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 5

2. © 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) 5, Ad1B

3. © 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. 5, Ad1B

4. © 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 5, Ad1B

5. © A Very Good Teacher 2007 Quadratic Transformations, cont… Effects on c Increasing c shifts the graph up Decreasing c shifts the graph down 5, Ad1C

6. © A Very Good Teacher 2007 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? 5, Ad1D 4 seconds

7. © 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 5, Ad2A

8. © A Very Good Teacher 2007 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 5, Ad2A, Ad2B

9. © 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 5, Ad2A, Ad2B

10. © 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) 5, Ad3A

11. © 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 5, Ad3A What’s left?

12. © 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 = 5, Ad3A