10.1 Graphing Quadratic Functions

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Quadratic Functions

Definition: a function described by an equation of the form f(x) = ax2 + bx + c , where a ≠ 0.

Examples:

y = 3x2 - 2x + 1 f(x) = -5x2 + 9

g(x) = -7x2 y = x2 + 4x + 2

Quadratic Functionsf(x) = ax2 + bx + c

When a is positive When a is negative

Use a table of values to graph the Quadratic Function y = 2x2 - 4x - 5

x y

-2 11

-1 1

0 -5

1 -7

2 -5

3 1

4 11

Use a table to graph the Quadratic Function y = -x2 + 4x - 1

x y

Vertex and Axis of SymmetryVertex: The coordinate of the maximum or minimum point. **Find the axis of symmetry first, then plug into equation and find y coordinate.

Axis of Symmetry: The x value of the vertex.To find the axis of symmetry:GIVEN: y = ax2 + bx + c

x =

Graphing Quadratic Functions

a) Write the equation for the axis of symmetry.x =

b) Find the coordinates of the vertex.Use x (axis of sym) to find y.

c) Identify the vertex as a maximum or minimum.

Is a positive (min) or negative (max)?d) Graph the function.

Graph f(x) = -3x2 - 6x + 4

Graph f(x) = -3x2 - 6x + 4