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Graphing Quadratic Functions (Complete)

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Math Algebra

on 4 January 2013

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Transcript of Graphing Quadratic Functions (Complete)

Get Ready for the lesson A band's manager figures that the up coming performance will be... f(x) = ax^2 + bx + c Where "x" is the price of one ticket Example Graph a Quadratic Graph f(x) = 2x^2 - 8x +9 x 2x^2 - 8x + 9 f(x) (x, f(x)) 0 1 2 3 4 2(0)^2 - 8(0) + 9 2(3)^2 - 8(3) + 9 2(4)^2 - 8(4) + 9 2(2)^2 - 8(2) + 9 2(1)^2 - 8(1) + 9 9 3 1 3 9 (0,9) (1,3) (2,1) (3,3) (4,9) parabola Quadratic stuff y = ax^2 + bx + c Axis of Symmetry: Middle of the "valley" Vertex: y = x^2 -- very bottom y = -x^2 -- very top Concept y x y = ax^2 + bx + c Quadratic term { { Linear term Constant term { o Axis of Symm. Y - intercept, Vertex, Roots AoS = -(b/2a) y = x^2 + 9 + 8x AoS = -(8/2(1)) AoS = -4 (x,y) x = -(b/2a) Vertex y - intercept x x^2 + 8x + 9 f(x) (x, f(x)) -6 -5 -4 -3 -2 (-6)^2 + 8(-6) + 9 (-5)^2 + 8(-5) + 9 (-3)^2 + 8(-3) + 9 (-2)^2 + 8(-2) + 9 (-4)^2 + 8(-4) + 9 -3 -6 -7 -6 -3 (-6,-3) (-5,-6) (-4,-7) (-3,-6) (-2,-3) (-4,-7) vertex Minimum value is "y" AoS = -(b/2a) f(x) = x^2 - 4x +9 (+)x means min AoS = -(-4/2(1)) AoS = 2 f(x) = x^2 - 4x + 9 f(2) = (2)^2 - 4(2) + 9 f(2) = 5 Domain and range Domain is all real numbers Range is all real numbers greater than or equal to the minimum value {f(x) | f(x) > 5} 5- 1 Graphing Quadratic Functions
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