Class Notes

Topics Covered

Finding the vertex, intercepts, and axis of symmetry from the graph of a parabola
Determining if graphs have symmetry with respect to the x-axis, y-axis, or origin
Testing an equation for symmetry about the axes and origin
Finding local maxima and minima of a function given the graph
Finding the absolute maximum and minimum of a function given the graph
Finding values and intervals where the graph of a function is zero, positive, or negative
Graphing an absolute value equation of the form y = A|x|
Graphing a cubic function of the form y = ax3
Graphing a function of the form f(x) = ax2
Graphing a function of the form f(x) = ax2 + c
Graphing a parabola of the form y = (x-h)2 + k
Graphing a square root function: Problem type 1
Graphing a cube root function
Translating the graph of a parabola: One step
Translating the graph of a parabola: Two steps
How the leading coefficient affects the shape of a parabola
Translating the graph of an absolute value function: One step
Translating the graph of an absolute value function: Two steps
How the leading coefficient affects the graph of an absolute value function
Writing an equation for a function after a vertical translation
Translating the graph of a function: One step
Translating the graph of a function: Two steps
Transforming the graph of a function by reflecting over an axis
Transforming the graph of a function by shrinking or stretching
Transforming the graph of a function using more than one transformation
Transforming the graph of a quadratic, cubic, square root, or absolute value function