Graphing Quadratic Equations
Objective Learn geometric properties of a
parabola, the graph of a general quadratic function, including
the axis of symmetry and the coordinates of the vertex.
You will be introduced to the shape of the graph of a
quadratic function. In so doing, you will be introduced to the
line of symmetry and the vertex. You will also be asked to
compute values using quadratic equations.
Quadratic Equations
Remember that a linear equation is an equation that involves a
single x term (with a coefficient), and a constant term:
y = ax + b.
Also recall that the graph of a linear equation is a line.
A quadratic equation is an equation that not only involves an
x term and a constant term like a linear function, but it also
has an x 2 term.
Definition of Quadratic
Function A quadratic function is a function that can be
described by an equation of the form y = ax 2 + bx + c
, where a  0.
The graphs of all quadratic functions have the same shape.
This shape is called a parabola.
Graphing Parabolas
The most basic parabola is the graph of the function y = x
2.
Let's make a table like the one below.
| x |
y = x
2 |
y |
| -2 |
(-2) 2 |
4 |
| -1 |
(-1) 2 |
1 |
| 0 |
(0) 2 |
0 |
| 1 |
(1) 2 |
1 |
| 2 |
(2) 2 |
4 |
Then plot the points and draw the graph.
Now let's plot points and draw the graphs of slightly more
complicated functions.
Example
Graph y = - 2 x 2 - 4 x .
Solution
| x |
y = -2x
2 - 4x |
y |
| -3 |
-2(-3) 2 -4(-3)
|
-6 |
| -2 |
-2(-2) 2 -4(-2) |
0 |
| -1 |
-2(-1) 2 -4(-1) |
2 |
| 0 |
-2(0) 2 -4(0) |
0 |
| 1 |
-2(1) 2 -4(1) |
-6 |
|