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EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x 2 + 12x – 7. a. Find the axis of symmetry of the graph of the function. b. Find the vertex of the graph of the function.

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EXAMPLE 1 Find the axis of symmetry and the vertex SOLUTION 12 2(– 2) x = –x = – b 2a = = 3= 3 Substitute – 2 for a and 12 for b. Then simplify. For the function y = –2x 2 + 12x – 7, a = 2 and b = 12. a. b. The x- coordinate of the vertex is, or 3. b 2a – y = –2(3) 2 + 12(3) – 7 = 11 Substitute 3 for x. Then simplify. ANSWER The vertex is (3, 11).

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EXAMPLE 2 Graph y = ax 2 + bx + c Graph y = 3x 2 – 6x + 2. Determine whether the parabola opens up or down. Because a > 0, the parabola opens up. STEP 1 STEP 2 = Find and draw the axis of symmetry: x = – b 2a2a – – 6– 6 2(3) =1. STEP 3 Find and plot the vertex.

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EXAMPLE 2 To find the y- coordinate, substitute 1 for x in the function and simplify. y = 3(1) 2 – 6(1) + 2 = – 1 So, the vertex is (1, – 1). STEP 4 Plot two points. Choose two x- values less than the x- coordinate of the vertex. Then find the corresponding y- values. Graph y = ax 2 + b x + c The x- coordinate of the vertex is b 2a2a, or 1. –

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EXAMPLE 2 Standardized Test Practice x 0 – 1 y 211 STEP 5 Reflect the points plotted in Step 4 in the axis of symmetry. STEP 6 Draw a parabola through the plotted points.

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EXAMPLE 2 Graph y = ax 2 + b x + c

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GUIDED PRACTICE for Examples 1 and 2 1. Find the axis of symmetry and vertex of the graph of the function y = x 2 – 2x – 3. ANSWER x = 1, (1, –4). 2. Graph the function y = 3x 2 + 12x – 1. Label the vertex and axis of symmetry. ANSWER

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