Quadratic Functions Unit 6

Linear vs. Quadratic Functions A linear function is represented as f(x) = x, where x is raised to the first power. A quadratic function is represented as , where x is raised to the second power.

Quadratic Functions A quadratic function represents a parabola. The general form for a quadratic is:

Graphing To create the graph of a quadratic function, use a table of values. *Remember the transformation/translation rules to make it easier!

Examples: Graph the following using a table of values.

Solving for missing coefficients Use the given equation and the point which the graph passes through to solve for the missing variable.

Assignment: Complete WS 1 #1-13 all & WS 2.1 (4 graphs)

The role of “a” The “a” values determines if the parabola opens up or down and how “wide” or “narrow” the parabola will be. If a > 0, the parabola opens up and the vertex is the lowest point (minimum). If a < 0, the parabola opens down and the vertex is the highest point (maximum).

The role of “c” If b=0, then (0, c) is the vertex The “c” value determines if the parabola is moved up or down vertically.

The role of “b” The “b” value moves the parabola horizontally If b = 0, then the parabola’s vertex is on the y-axis.

Identify the a, b, and c values.

Assignment: WS 2.2 (front)

Vertex To find the vertex of a parabola, you can: 1. Use the formula to find the x-coordinate, and then evaluate the function to find y. 2. Complete the square to fit the vertex form.

Vertex Form Where (h, k) is the vertex

Axis of Symmetry The axis of symmetry is the vertical line that divides the parabola into to halves. It is the form x = h, where h is the x-coordinate of the vertex. If b=0, then the axis of symmetry is the y-axis.

Point of Symmetry The point of symmetry is the ordered pair that is symmetrical to the y-intercept. Use the form: to find the point.

Intercepts To find the y – intercept, find f(0). To find the x – intercepts, factor or solve for x. (This is also called finding the zeros)

Find the vertex, intercepts, axis of symmetry, and the point of symmetry.

Assignment: Complete WS 3 #1-8 all