Graphing Quadratic Functions

Vertex Form Root Form Standard Form

Plot the vertex

Axis of symmetry is the line Use the value to plot additional points. Minimum or Maximum value is To find y-intercept, substitute 0 in for and

solve for . To find x-intercepts, substitute 0 in for and

solve for .

Plot the x-intercepts, and .

Find the vertex using the roots, .

Substitute in for and solve for . The value for that is found is the value.

Plot the vertex .

Axis of symmetry is the line

Minimum or Maximum value is To find y-intercept, substitute 0 in for and

solve for .

Find the vertex using . Substitute

in for and solve for . The value for that is found is the value.

Plot the vertex .

Axis of symmetry is the line Use the value to plot additional points. Minimum or Maximum value is

The y-intercept is .

To find x-intercepts, substitute 0 in for and solve for .

Vertex:__________ Axis of Sym____________

min or max value ______

y-intercept________ x-int _________________

Domain_____________Range_______________

Vertex:__________ Axis of Sym____________

min or max value ______

y-intercept________ x-int _________________

Domain_____________Range_______________

Vertex:__________ Axis of Sym____________

min or max value ______

y-intercept________ x-int _________________

Domain_____________Range_______________

Using the value

If , the function will have a maximum value. If , the function will have a minimum value.

Sketch the graph of a quadratic function using the Counting Pattern: over 1, up

over 1, up

over 1, up etc.

To find the x-intercepts of a quadratic function, , solve the equation . Recall the discriminant,

tells us how many solutions and the nature of the solutions. The discriminant therefore gives us information about the x- intercepts.

Using Vertex form to describe Transformations of the parent function

Reflection over the axis

Vertical Stretch

Vertical Shrink

Horizontal slide left subtract from the coordinates

Horizontal slide right add to the coordinates

Vertical slide down subtract from the coordinates

Vertical slide up add to the coordinates

the reflection and the stretch or shrink can be applied at the same time simply by multiplying the coordinates by