Quadratic Graphs – Day 2 Warm-Up:

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Presentation transcript:

Quadratic Graphs – Day 2 Warm-Up: Find the turning point and roots of each parabola without a calculator y = x2 – 8x + 1 y = -x2 – 6x - 2

Quadratic Graphs – Writing the Equation Standard Form: y – y1 = a(x – x1)2 (x1, y1) will be the turning point of the graph Must find a value to complete equation. Similar to finding “b” value in y = mx + b Example: A parabola has a turning point of (1,2) and also passes through the point (3, -6) Find its equation

Quadratic Graphs – Writing the Equation Practice Turning Point (4,-1) Passes through the point (2,3) Vertex (2,3) Passes through the point (0,2) Turning Point (-2,-2) Passes through the point (-1,0) Vertex (5/2, -3/4), passes through the point (-2,4)

Quadratic Graphs – Writing the Equation Practice Turning Point (5,-6) Passes through the point (1,3) Vertex (2,3) Passes through the point (0,4) Turning Point (-2, 2) Passes through the point (-3,0) Vertex (7/2, -1/4), passes through the point (-5,3)

Quadratic Graphs – Applications Flight of an Object The height of a football punted on 4th down is given by the equation: y = -16/2025 x2 + 9/5 x + 1.5 where x is the distance in feet covered horizontally along the field. a) How high is the ball when punted? b) What is the maximum height of the punt? c) How far does the punt travel?

Quadratic Graphs – Applications Maximum Profit The profit that a certain company makes is dependent on the amount of advertising they do for their product. Profit follows the equation: P = 230+ 20x - .5x2 Where p is profit and x is $ spent on advertising. What amount of advertising will yield a maximum profit?

Quadratic Graphs – Applications Maximum Revenue Total Revenue earned (in thousands of dollars) from manufacturing hand-held smartphones is given by: R(x) = -25x2 + 1200x Where x is the price per unit Find revenue when price is $20, $25, $30 What price will result in the maximum revenue? What is the maximum revenue?