1. 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

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

3. 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)

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)

5. Quadratic Graphs – Applications
Flight of an Object
The height of a football punted on 4th down is given by the equation:
y = -16/2025 x /5 x
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?

6. 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 = x - .5x2
Where p is profit and x is $ spent on advertising.
What amount of advertising will yield a maximum profit?

7. Quadratic Graphs – Applications
Maximum Revenue
Total Revenue earned (in thousands of dollars) from manufacturing hand-held smartphones is given by:
R(x) = -25x x
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?