Today:

Final Review for FinalBring Notebooks Tomorrow

Class Work from Friday, Monday, & today, due tomorrow (last 3rd Qtr.

Grade)

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.

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.

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??

Holt Algebra 1

9-3 Graphing Quadratic FunctionsAfter 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.

Find1. 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.

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, and3. 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)

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......

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.

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.

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).

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)

Holt Algebra 1

9-3 Graphing Quadratic FunctionsThe 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.

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?