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Quadratic Functions

Quadratic Functions. Quadratic Function. A function written in the form f(x) = ax 2 + bx + c , where a  0. quadratic term. linear term. constant term. Classifying Functions. Determine whether each function is linear or quadratic. Identify the quadratic, linear and constant term.

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Quadratic Functions

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  1. Quadratic Functions

  2. Quadratic Function A function written in the form f(x) = ax2 + bx + c, where a 0. quadratic term linear term constant term

  3. Classifying Functions Determine whether each function is linear or quadratic. Identify the quadratic, linear and constant term. 1. f(x) = (x – 5)(3x – 1) 2. f(x) = (x2 + 5x) – x2 3. f(x) = x(x + 3) quadratic; 3x2, -16x, 5 Linear; none, 5x, none quadratic; x2, 3x, none

  4. PARABOLAGraph of a Quadratic Function Parabola Vertex Axis of symmetry A vertical line that divides a parabola into two parts that are mirror images. x = 7 The point at which the parabola intersects the axis of symmetry. The y value of the vertex represents the maximum or the minimum value of the function. Equation: (7, -9) -9 minimum value x value of the vertex

  5. Finding a Quadratic Model Find a quadratic model for each set of values. • (1, -2), (2, -2), (3, -4) • (1, -2), (2, -4), (3, -4) 3. (-1, 6), (1, 4), (2, 9) f(x) = -x2 + 3x – 4 f(x) = x2 – 5x + 2 f(x) = 2x2 – x + 3

  6. Real – World Connection A man throws a ball off the top of a building. That table shows the height of the ball at different times. • Find a quadratic model for the data. • Use the model to estimate the height of the ball at 2.5 seconds. • After how many seconds will the ball be at 20 ft? Height of the Ball • y = -16x2 + 33x + 46 , where x is the number of seconds after release and y is height in feet. • The ball will be 28.5 ft after 2.5 seconds. • Approximately 2.7 seconds.

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