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9.3 Graphing Quadratic Functions

9.3 Graphing Quadratic Functions. Quadratic Functions. Quadratic functions are functions written in the form Every quadratic function has a U-shaped graph called a parabola. y = ax 2 +bx + c When a>0, the parabola opens up. The vertex is the minimum point.

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9.3 Graphing Quadratic Functions

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  1. 9.3 Graphing Quadratic Functions

  2. Quadratic Functions • Quadratic functions are functions written in the form • Every quadratic function has a U-shaped graph called a parabola.

  3. y = ax2 +bx + c When a>0, the parabola opens up. The vertex is the minimum point. Positive a = smiley face  Axis of Symmetry Vertex If the leading coefficient is positive, the parabola opens up, like a U.

  4. y = ax2 +bx + c When a<0, the parabola opens down. The vertex is the maximum point. Negative a = Sad Face  Axis of Symmetry Vertex If the leading coefficient is negative, the parabola opens down, like an upside-down U.

  5. Parabolas • The lowest/highest point on a parabola is called the vertex. • The axis of symmetry is the line that runs through the vertex and divides the parabola in two symmetric parts. • The x-coordinate of the vertex, and the equation of the axis of symmetry will be the line x = -b 2a

  6. GRAPHING QUADRATIC EQUATIONS • Make a table • Plot points and connect dots to make a smooth curve.

  7. Quadratic Functions will be in the form y = ax2 + bx + c or f(x) = ax2 + bx + c The graph of a Quadratic Function will be a parabola.

  8. Use the table with the given values for x to find f(x). Then graph the function • y = x2

  9. y = 2x2 y = -2x2

  10. Graph each function, and compare them to the graph of y = x2 y = 5x2 y = ¼ x2

  11. y = 5x2 Do you notice any patterns here? y = x2 As the coefficient (a) of x2 gets larger, the graph gets narrower; And if the coefficient is less than 1, the graph is wide. y = ¼ x2

  12. Homework Section 9.3Page 521, # 5-10, and # 11,12,14,15,19Plus, Box and Whisker Question on Handout (See page 375)BONUS: Do p. 378, #8-10,#15-17

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