Download M098 Carson Elementary and Intermediate Algebra 3e Section 6.7 Objectives

M098
Carson Elementary and Intermediate Algebra 3e
Section 6.7
Objectives
1.
2.
2
Graph quadratic equations in the form y = ax + by + c (using a table).
Graph quadratic functions (using a table).
Vocabulary
Axis of symmetry
Vertex
Parabola
A line that divides a graph into two symmetrical halves.
The lowest point on a parabola that opens up or highest point on a parabola that opens
down.
The shape of the graph of a quadratic equation.
Prior Knowledge
Graphing equations using a table of values.
Function notation: y = f(x)
Vertical line test
New Concepts
2
1. Graph quadratic equations in the form y = ax + bx + c
The graphing that we did earlier involved linear equations in two variables. The highest degree of any
term was 1. The graph of a linear equation is a straight line.
Now we want to look at the graphs of quadratic (degree 2) equations.
One method that always works to graph an equation is to create a table of values.
Example 1: Graph y = x
x
-2
-1
0
1
2
2
y
4
1
0
1
4
Axis: x = 0
Vertex (0, 0)
The graph of every quadratic equation will be in the shape of a parabola. The axis of symmetry is the
vertical line that divides the graph into two symmetrical halves. The vertex is the lowest or highest point of
the parabola.
Example 2: Graph
x
-2
1
0
1
2
V. Zabrocki
y
9
3
1
3
9
2
y = 2x + 1
Axis: x = 0
Vertex: (0, 1)
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M098
Carson Elementary and Intermediate Algebra 3e
Example 3: Graph
x
y
2
8
1
1
0
4
1
1
2
8
Section 6.7
2
y = – 3x + 4
Axis: x = 0
Vertex: (0, 4)
Notice that the sign of the coefficient of the squared term indicates the direction of the parabola:
If a > 0, the parabola opens upward.
If a < 0, the parabola opens downward.
Also notice that the constant is the y-intercept when the equation is written in standard form:
2
y = ax + bx + c
By looking at the graph of a quadratic equation, which is a parabola, we can see that quadratic equations
2
are functions. Each x-value has one and only one y-value. Instead of writing y = ax + bx + c, we can also
2
write f(x) = ax + bx + c. Graphing a quadratic function is the same as graphing a quadratic equation.
V. Zabrocki
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