1. Today:
Final Review for Final
Bring Notebooks Tomorrow
Class Work from Friday, Monday, & today, due
tomorrow (last 3rd Qtr. Grade)
2. Warm-Up/Review:
1. Parabola’s which have one solution (actually two
identical solutions), are always the graphic form of
what type of equation.
2. Complete the factored
form of this PST (x )2
3. Finally, write the original
equation for the parabola
shown.
3. Warm-Up/Review:
4. A graph of a quadratic function has x intercepts
of (-5,0) and (3,0). What is the axis of symmetry?
The half-way point between two solutions is always the
axis of symmetry.
5. Find the vertex and four other points, then draw the
parabola.
4. Warm-Up/Review (2):
The path of many thrown or fired
objects
(balls, rocks, missiles, etc.), is
parabolic. Each has a vertex
_________.
All versions of the final will have one of each of these last
two types of problems. Every version will have one of each.
1. What are the dimensions of the length and width?
What does the vertex of all
these parabolas tell us?
Will any parabola of a thrown or fired
object have a solution or solutions??
5. Holt Algebra 1
9-3 Graphing Quadratic Functions
After a player takes a shot, the height in feet of a basketball
can be modeled by f(x) = –16x2 + 32x, where x is the time in
seconds after it is shot. Find
1. The basketball’s maximum height
2. The time it takes the basketball to reach this height.
3. How long the basketball is in the air.
There is no c term in this equation. What does
that tell us about our graph??
The graph is not shifted up or down the y axis, therefore
the y-intercept is at the origin, which also means one of
the solutions must be zero.
6. Holt Algebra 1
9-3 Graphing Quadratic Functions
1 Understand the Problem
Our answer includes three parts:
1. The maximum height of the ball,
2. The time to reach the maximum height, and
3. The time to reach the ground.
• The function f(x) = –16x2 + 32x models the height of
the basketball after x seconds.
List the important information:
What are the two variables for our x and y axes.
(Plural of axis, pronounced ax-eez)
7. Holt Algebra 1
9-3 Graphing Quadratic Functions
2 Make a Plan
The basketball will hit the ground when its height is 0.
Round to the nearest whole number if necessary.
What parts of the graph are important in solving our problem?
A. The vertex. Why?
A. Because the maximum height of the basketball and the
time it takes to reach it are the coordinates of the vertex.
B. The zero's of the function because......
8. Holt Algebra 1
9-3 Graphing Quadratic Functions
Solve3
Step 1 Find the axis of symmetry.
Use x = . Substitute
–16 for a and 32 for b.
Simplify.
The axis of symmetry is x = 1.
9. Holt Algebra 1
9-3 Graphing Quadratic Functions
Step 2 Find the vertex.
f(x) = –16x2 + 32x
= –16(1)2 + 32(1)
= –16(1) + 32
= –16 + 32 = 16
The vertex is (1, 16).
The x-coordinate of
the vertex is 1.
Substitute 1 for x.
Simplify.
The y-coordinate is 16.
10. Holt Algebra 1
9-3 Graphing Quadratic Functions
Step 3 Find the y-intercept.
Identify c.f(x) = –16x2 + 32x + 0
The y-intercept is 0; the graph passes through (0, 0).
11. Holt Algebra 1
9-3 Graphing Quadratic Functions
Step 4: Graph the axis of symmetry, the vertex, and the point
containing the y-intercept. Then use symmetry to reflect the
point across the axis of symmetry. Connect the points with a
smooth curve.
(0, 0)
(1, 16)
(2, 0)
12. Holt Algebra 1
9-3 Graphing Quadratic Functions
The vertex is (1, 16). So at 1 second, the basketball has
reached its maximum height of 16 feet.
(0, 0)
(1, 16)
(2, 0)
The graph shows the zero’s of the function are 0 and 2. At 0
seconds the basketball has not yet been thrown, and at 2 seconds
it reaches the ground. The basketball is in the air for 2 seconds.
13. Class Work: 2 problems, add to Friday &
Monday’s document.
1. What are the dimensions of the length and width?
2. You throw a ball which
travels along the path
y = -x2 + 13x + 40, where x & y
are both measured in feet.
Graph the function, then
answer the following:
a) What was the
maximum height of
the ball
b) How far did the ball travel
before hitting the ground?
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