Quadratic Functions

Quadratic Functions Integrated Math 4 Mrs. Tyrpak

Definition of Quadratic Function Let a, b, and c be real numbers with then is called a quadratic function.

Characteristics Vertex: Axis of Symmetry: Graph: parabola, if a > 0 then it faces up and if a < 0 it faces down

Finding the Vertex Find the vertex and describe the graph:

Maximums and Minimums A textile manufacturer has daily production costs of where C is the cost in dollars and x is the number of units produced. How many fixtures should be produced each day to yield a minimum cost?

Solution

Vertex Form Vertex: (h, k) Axis of symmetry: x = h Graph: same as the definition

Finding the x-intercepts *Also called the zeros or the roots *Methods Used: • Graphing • Factoring • Principle of Square Roots • Completing the Square • Quadratic Formula

Review Since all of these methods should be review from your previous math courses we will review each by looking at an application of the last four.

Factoring You have made a rectangular stained glass window that is 2 feet by 4 feet. You have 7 square feet of clear glass to create a border of uniform width around the window. What should the width of the border be? *Take 1 minute to draw a picture

Picture

Solution Border Area= Total Area – Window Area

Principle of Square Roots The equation gives the height h (in feet) of the largest ocean waves when the wind speed is s knots. How fast is the wind blowing if the largest waves are 15 feet high.

Completing the Square Find the vertex of the following parabola by writing it in standard form.

Quadratic Formula The length l (in feet) of runway needed for a small airplane to land is given by where s is the airplane’s speed in feet per second. If a pilot is landing a small airplane on a runway 2000 feet long, what is the maximum speed at which the pilot can land?

Solution

Thanks for your attention! Don’t forget to complete both the extension and enrichment assignments before you move on. Keep up the hard work!

Quadratic Functions