Section 3.1 Quadratic Functions

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Presentation transcript:

Section 3.1 Quadratic Functions

Graphs of Quadratic Functions

Graphs of Quadratic Functions Parabolas Vertex Minimum Maximum Axis of symmetry

Graphing Quadratic Functions in Standard Form NOTE: I do not know why this book calls this the standard form when every other book calls it the “Vertex” form.

Seeing the Transformations

Using Standard Form a<0 so parabola has a minimum, opens down

Example Graph the quadratic function f(x) = - (x+2)2 + 4.

Example Graph the quadratic function f(x) = (x-3)2 - 4

Graphing Quadratic Functions in the Form f(x)=ax2+bx+c

Using the form f(x)=ax2+bx+c a>0 so parabola has a minimum, opens up

Example Find the vertex of the function f(x)=-x2-3x+7

Example Graph the function f(x)= - x2 - 3x + 7. Use the graph to identify the domain and range.

Minimum and Maximum Values of Quadratic Functions

Example For the function f(x)= - 3x2 + 2x - 5 Without graphing determine whether it has a minimum or maximum and find it. Identify the function’s domain and range.

Applications of Quadratic Functions

Example You have 64 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

(a) (b) (c) (d)

(a) (b) (c) (d)