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Warm-Up Find a linear function that describes the situation, and solve the problem. 4 minutes 1) A tractor rents for $50, plus $5 per engine hour. How much does it cost to rent and run the tractor for 6 hours?

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12.4 Quadratic Functions 12.4 Quadratic Functions Objectives: To graph quadratic functions

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Graphs of Quadratic Functions Using a graphing calculator, graph the equation y = x 2. What is the lowest point on the graph? Which axis divides the graph in half? (0,0) y-axis Using a graphing calculator, graph each of the following equations. y = 2x 2 y = 2x 2 + 1 y = 2x 2 – 4x

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Quadratic Function A function f defined by an equation of the form y = ax 2 + bx + c, where a,b, and c are real numbers and a = 0, is a quadratic function and can be written f(x) = ax 2 + bx + c. The graph of a quadratic function is called a parabola.

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Example 1 Graph the quadratic function f(x) = -x 2. f(x) = -x 2 xf(x) -2 0 1 2 -4 0 -4 x y

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Example 1 Graph the quadratic function f(x) = -x 2. x y The vertex is the maximum or minimum point of a parabola. vertex If the graph of a parabola is folded so that the two sides of the parabola coincide, then the fold line is the axis of symmetry. axis of symmetry

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Vertex and Axis of Symmetry For a parabola defined by the equation y = ax 2 + bx + c: 1)the x-coordinate of the vertex is 2) the axis of symmetry is the line

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Example 2 Find the vertex and axis of symmetry, then graph the quadratic function f(x) = 2x 2 - 8x + 4. x y y-coordinate of vertex: y = 2x 2 – 8x + 4 = 2(2) 2 – 8(2) + 4 = 8 – 16 + 4 = -4 vertex: (2,-4)

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Example 2 Find the vertex and axis of symmetry, then graph the quadratic function f(x) = 2x 2 - 8x + 4. x y axis of symmetry: x = 2 f(x) = 2x 2 – 8x + 4 xf(x) 0 1 2 3 4 4 -2 -4 -2 4

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Practice Find the vertex and axis of symmetry, then graph the function. 1) f(x) = -2x 2 + 4x + 1 2) g(x) = x 2 -3x + 1

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Homework p.554-555 #1-19 odds

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