GRAPHING QUADRATICS QUIZ REVEW NAME:

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Jayson Bruce
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1 GRAPHING QUADRATICS QUIZ REVEW NAME: USE THE CALCULATOR to graph the following functions and determine the key features. 1. y = 2 (x + 1) y = ½x 2 + 4x 1 : / Factor: : / Factor:

2 3. Complete without a calculator =) EQUATION A y = ( x 3) B y = 3( x 4) 2 1 C y = 2x D y = 2 ( 3 x 10 ) 2 9 OPEN E y = ( x +1) 2 F y = 5 2 x 2 8 G y = 2( x 5) 2 H y = 80( x + 2) VERTEX (initial point) 4. Circle each function with the same RANGE as y = x. SHIFT (horizonal/vertical) VERTICAL CHANGE y = x 7 y = x 2 y = x + 2 y = (x + 2) Circle each function that has an ABSOLUTE MINIMUM at its vertex. y = x + 2 y = x 2 y = x y = (x + 2) Circle each function that is shifted to the RIGHT. y = 1 2 x 5 y = (x + 2)2 4 y = (x 9) 2 y = 1 3 x 5 7. Circle each function that is a vertical SHRINK. y = 1 3 x 2 10 y = 2 x + 2 y = 7 2 (x 1)2 + 5 y = 1 (x 2)2 2

3 8. FIND THE VERTEX OF EACH FUNCTION: NO CALCULATOR =) Function Form Work Range A y = (x + 4) 2 10 B y = x 2 + 4x + 5 C y = 3(x 1)(x 3) D y = 2x 2 20x + 40 E y = 3(x 2) F y = ( x + 4) ( x 10) G y = (x + 2)(x 4) H y = 2x 2 8x + 1 I y = 2( x + 4) ( x 10) J y = (x + 4) 2

4 9. y = 2 (x + 3) 2 8 NO CALCULATOR SECTION =) 10. y = 2 (x + 1) (x 3) : / Factor: : / Factor:

5 11. y = x 2 6x 9 NO CALCULATOR SECTION =) 12. y = 2x 2 8x + 9 : / Factor: Relative Minimum: Relative Maximum: : / Factor: Relative Minimum: Relative Maximum:

6 Find the solutions (zeros) of the functions algebraically. 13. y = (x + 3) y = 2 (x + 1) y = (x + 5) (x 10) 16. y = 3 (2x 5) (3x 8) 17. y = 8x y = x 2 + 5x 14

7 19. Create a quadratic function that: Equation: o Opens down o Is a vertical shrink o Is shifted right 2 o Is shifted down 9 Convert each function to standard form. 20. y = 2 (x + 1) (x 5) 21. y = 3 (x 4) Convert each function to intercept form. 22. y = x 2 + x y = 2x 2 18

8 #24 & 25 Given the graph, write the quadratic equation for each of the following: y y x x Thevertexis. Theinterceptsare. Equation: Equation: 26. Use the calculator to do a regression and answer the questions:

9 NO CALCULATOR Table: 4/5 Form Direction Dilation Domain/Range 4 Graphs (1 of each) Axis of Symmetry Direction Zeros Inc/Dec End behavior Domain/Range y-intercept Max/Min (not ordered pair only y-value just the number) No Solution (no zeros) 2 Solutions is on the x-axis CALCULATOR (2 questions) standard form + vertex form Zeros not integers Bonus: regression Bonus: Write an equation of the graph (a-value) Solving Equations: square roots, zero product, factoring A cannot be 0.

10 KEY FEATURES OF GRAPHS Use the Calculator to Graph 1. f (x) = 3x(x 2) 2. g (x) = 2 (x + 1) 2 5 x -intercepts: Axis of Symmetry: : : Axis of Symmetry: : Domain: Range: Increasing: Decreasing: Zeroes: Y-intercept: Domain: Range: Increasing: Decreasing: Zeroes: Y-intercept: Maximum Value of f(x): Minimum Value of f(x): Maximum Value of g(x): Minimum Value of g(x):

11 #3 &4 Given the graph, write the quadratic equation for each of the following: y y x x Thevertex: Thex intercept(s)is/are Thefactorsare Thefactorsare Otherpoint: Otherpoint: Equation: Equation:

Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections 3.1, 3.3, and 3.5

Department of Mathematics, University of Wisconsin-Madison Math 11 Worksheet Sections 3.1, 3.3, and 3.5 1. For f(x) = 5x + (a) Determine the slope and the y-intercept. f(x) = 5x + is of the form y = mx