Today's lesson reviews graphing quadratic functions by examining how the b value changes the parabola's position. The teacher discusses important concepts from the previous day like the axis of symmetry and vertex. Students learn that a positive b value results in a shift of the parabola to the left. For class work, students will practice graphing quadratic functions by finding the axis of symmetry and vertex, then plotting additional points to complete the parabola.

1. Holt Algebra 1
9-3 Graphing Quadratic Functions
TGIF April 4, 2014
Today:
 Review from Yesterday
 Getting to Know the Quadratic Function:
(how the b value changes the parabola)
 Class Work

2. Holt Algebra 1
9-3 Graphing Quadratic Functions
Important Concepts from Yesterday:
1. There is no single "right way" to graph a quadratic
function.
In fact the goal is for you to understand and use a variety
of methods, so that you can choose the best (easiest)
method for a given problem.
2. The axis of symmetry is an important part of parabolas
and can save you much time and effort if you understand
its properties.
Because a parabola is symmetrical, each point is the
same number of units away from the axis of symmetry.
Helpful Hint
2.5 You must have at least 5
points to graph the parabola.

3. Holt Algebra 1
9-3 Graphing Quadratic Functions
4. The vertex is an (x,y) coordinate on the AOS, and is
either the minimum or maximum y value
Important Concepts from Yesterday:
5. The vertex is an (x,y) coordinate on the AOS, and is
either the minimum or maximum y value
6. All parabolas begin from the parent function (y = x2),
and are moved around the coordinate plane from changes
in the a, b, and c values.
3. The axis of symmetry has a single coordinate (x) and
represents the exact center of the parabola.
7. A quadratic equation with no solutions will not cross
the x-axis at any point. It can still be graphed using other
methods.

4. Holt Algebra 1
9-3 Graphing Quadratic Functions
Review from Yesterday:
How the a and c values affect the quadratic
function y = ax2 + bx + c
Start with the parent function, which is...
First, how does a change in a affect the parabola
y = x2
Effects of the a, b, & c values

5. Holt Algebra 1
9-3 Graphing Quadratic FunctionsEffects of the a, b, & c values
1. The greater the value
of 'a', the narrower and
steeper the graph.
2. A positive 'a' value
results in parabola
which turns up and has
a vertex minimum.
3. A negative 'a' value
results in parabola
which turns down and
has a vertex maximum.

6. Holt Algebra 1
9-3 Graphing Quadratic FunctionsEffects of the a, b, & c values
How does a change in c affect the parabola?
The value of c is also
used to find the
y-intercept.
Set the 'x' values = 0,
and find the intercept.
We would expect the
value of 'c' in this
graph to be.......

7. Holt Algebra 1
9-3 Graphing Quadratic Functions
Effects of the a, b, & c values
How changes in 'b' affect the parabola:
Why does a positive b value (see aqua, b = 2)
result in a shift 2 units to the left?

8. Holt Algebra 1
9-3 Graphing Quadratic Functions
Graph the quadratic function.
y = x2 + 4x + 4
Step 2 Find the axis of symmetry,
Step 1: Try to picture what the graph will look like before
you start. Use the a,b, and c values to determine your
prediction
Step 3: Determine the best method(s) to
solve that particular function.
Step 4 : Plot at least 5 points, then connect the dots to
complete the parabola.
then find 'y' to complete the coordinates for the vertex

9. Holt Algebra 1
9-3 Graphing Quadratic Functions
Step 2 Find the axis of symmetry and the vertex.
y = x2 + 4x + 2
Substitute for x to find the y coordinate
The x-coordinate of the vertex is...
The y-coordinate is
Find at least 4 more points, then graph.
This is also the AOS

10. Holt Algebra 1
9-3 Graphing Quadratic Functions
Step 5 Graph the axis of
symmetry, the vertex, the point
containing the y-intercept, and
two other points.
Step 6 Reflect the points
across the axis of
symmetry. Connect the
points with a smooth curve.
y = x2 + 4x + 2
Example 2 Continued

11. Holt Algebra 1
9-3 Graphing Quadratic Functions
Class Work:
Graphing Quadratic Functions

12. Holt Algebra 1
9-3 Graphing Quadratic Functions