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
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