CP ALG II 10/22/15
Graphing Quadratic Functions
Name:________________
Warm Up: Graph each function. Label the x-intercept(s), y-intercept, vertex, and find the equation for
the axis of symmetry. State the domain and range.
f (x) = ( x + 2) -1
f (x) = -2(x - 3)2 + 8
f (x) = 2 ( x -1) +1
1
f (x) = - x 2 - 2
2
2
2
VERTEX FORM:
f (x) = a ( x - h) + k
2
*where (h, k) is the vertex.
STANDARD FORM: f (x) = ax 2 + bx + c
How can we easily find the vertex from standard form?
AXIS OF SYMMETRY: The axis is symmetry is a vertical line that passes through the vertex of a
-b
parabola. It can be calculated from an equation in standard form with x =
.
2a
EX #1: For each quadratic function.
o Find the vertex. Is this point a maximum or a minimum?
o Sketch the graph.
o Rewrite the equation of the function in vertex form.
o State the domain and range.
a.
f (x) = x 2 - 8x +13
b.
f (x) = -2x 2 + 4x - 4
EX #2:
Identify the x and y-intercepts.
a.
f (x) =
2
1
x + 4) - 3
(
3
EX #3: Given: f (x) =
b.
f (x) = -2 ( x - 4) + 6
2
1 2
x - 4x + 6
2



Find the vertex. Is this point a maximum or minimum?
Write the equation in vertex form.
Find the x and y-intercepts.
Assignment: pg. 224 # 23, 24, 25, 27, 29, 31