Section 1-7:  Quadratic Functions - Graphs 
A quadratic function is in the form f(x) = ax2 + bx + c.  A quadratic function graphs into a parabola, a curve shape like the McDonald's arches.  Every quadratic function has a vertex and a vertical axis of symmetry.  This means it is the same graph on either side of a vertical line.  The axis of symmetry goes through the vertex point.  The vertex point is either the maximum or minimum point for the parabola.  A summary of what we talked about last year is shown below:


graph opens up 

graph opens down

b2 - 4ac > 0 

b2 - 4ac = 0 

b2 - 4ac < 0

Graph has 2 x-intercepts 

Graph has 1 x-intercept 

Graph has no x-intercepts

Vertex Point at x = -b/2a 

to find y substitute above 

value for x

x-intercepts factor or use quadratic formula
y-intercept c value in ax2 + bx + c

Sample Problems
Find the vertex point, axis of symmetry, x and y intercepts and graph.
1)  F(x) = x2 + 2x - 3
Solution:    The graph opens up because a is positive.
The vertex point is at x = -b/2a = -2/2 = -1
y = (-1)2 + 2(-1) - 3 = -4
Vertex point is at (-1, -4)
Axis of symmetry is the equation x = -1
x-intercepts found by factoring (x + 3)(x - 1) = 0
They are at x = -3, x = 1
y-intercept at (0, c) at (0, -3)
The graph is as follows:

Alternate method!
A second form of a quadratic can be written in the following form:
f(x) = a(x - h)2 + k Where (h, k) is the vertex point

Find the vertex point using the alternate method.

2nd Sample Problem!
Use the second method to graph the following equation!
The graph looks like this:

That concludes our review of quadratics and graphing.  On to quadratic modeling!!