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9.3 Graphing Quadratic Functions

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

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Axis of Symmetry Vertex y = ax 2 +bx + c When a>0, the parabola opens up. The vertex is the minimum point. Positive a = smiley face If the leading coefficient is positive, the parabola opens up, like a U.

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Axis of Symmetry Vertex y = ax 2 +bx + c When a<0, the parabola opens down. The vertex is the maximum point. Negative a = Sad Face If the leading coefficient is negative, the parabola opens down, like an upside-down U.

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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

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

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Quadratic Functions will be in the form y = ax 2 + bx + c or f(x) = ax 2 + bx + c The graph of a Quadratic Function will be a parabola.

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y = x 2 Use the table with the given values for x to find f(x). Then graph the function XY -2 0 1 2

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y = 2x 2 y = -2x 2

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Graph each function, and compare them to the graph of y = x 2 y = 5x 2 y = ¼ x 2 XY -220 5 00 15 220 XY -816 -44 00 44 816

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y = x 2 y = 5x 2 y = ¼ x 2 Do you notice any patterns here? As the coefficient (a) of x 2 gets larger, the graph gets narrower; And if the coefficient is less than 1, the graph is wide.

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

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