Quadratic Graphs – Day 2

• Warm-Up:• Find the turning point and roots of each

parabola without a calculator1.y = x2 – 8x + 12.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

1. Turning Point (4,-1) Passes through the point (2,3)

2. Vertex (2,3) Passes through the point (0,2)3. Turning Point (-2,-2) Passes through the point

(-1,0)4. Vertex (5/2, -3/4), passes through the point (-

2,4)5. Vertex (2,3) Passes through the point (0,2)

Quadratic Graphs – Writing the Equation Practice

1. Turning Point (5,-6) Passes through the point (1,3)

2. Vertex (2,3) Passes through the point (0,4)3. Turning Point (-2, 2) Passes through the point

(-3,0)4. 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?