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M.M. 10/1/08 What happens if we change the value of a and c ? y=3x 2 y=-3x 2 y=4x 2 +3 y=-4x 2 -2

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Graphing Quadratic Functions y = ax 2 + bx + c

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Vocabulary Minimum Value: the y-coordinate of the vertex when the parabola is open upwards Maximum Value: the y-coordinate of the vertex when the parabola is open downward

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y x Line of Symmetry The line of symmetry ALWAYS passes through the vertex. If we graphed one side of the parabola, we could “fold” (or REFLECT) it over, the line of symmetry to graph the other side.

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For example… Find the line of symmetry of y = 3x 2 – 18x + 7 Finding the Line of Symmetry When a quadratic function is in standard form The equation of the line of symmetry is y = ax 2 + bx + c, Using the formula… Thus, the line of symmetry is x = 3.

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Finding the Vertex We know the line of symmetry always goes through the vertex. Thus, the line of symmetry gives us the x – coordinate of the vertex. To find the y – coordinate of the vertex, we need to plug the x – value into the original equation. STEP 1: Find the line of symmetry STEP 2: Plug the x – value into the original equation to find the y value. y = –2x 2 + 8x –3 y = –2(2) 2 + 8(2) –3 y = –2(4)+ 8(2) –3 y = –8+ 16 –3 y = 5 Therefore, the vertex is (2, 5)

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Graphing a Quadratic Function in Standard Form There are 3 steps to graphing y = ax 2 + bx + c STEP 1: Find the line of symmetry STEP 2: Find the vertex STEP 3: Find two other points on either side of the axis of symmetry. Then connect the five points with a smooth curve. Plug in the line of symmetry (x – value) to obtain the y – value of the vertex. MAKE A TABLE using x – values close to the line of symmetry.

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STEP 1: Find the line of symmetry Try … y = 2x 2 – 4x – 1 Let's Graph ONE! Thus the line of symmetry is x = 1

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STEP 2: Find the vertex Thus the vertex is (1,–3). Since the x – value of the vertex is given by the line of symmetry, we need to plug in x = 1 to find the y – value of the vertex.

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5 –1 STEP 3: Find two other points on either side of the line of symmetry. Then connect the five points with a smooth curve. 3 2 yx Does the graph have a maximum or minimum value?

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Textbook p. 109-110 (1-9 odd, 15-19 odd, 27-30, 37-41 odd) Homework

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