Today:

Review all Quadratics for Test FridayNew Solving & Graphing Method: Square Roots

Complete Class Work from Friday

3rd Quarter Final Exam:

The exam is on Friday; be here. 10 Questions on:

A. Quadratics B. Factoring ax2 + bx + c polynomials

10 Questions on:C. Exponents

D. Adding, Subtracting, Multiplying & Dividing Monomials and Polynomials

Notebooks submitted Tues – Fri. (1st – 4th)

Warm-Up/Review:1. y = 5x2 – 1; Graph the general shape and location from the information given in the function. Width, shape, vertex, y-intercept, etc. Even the missing ‘b’ term provides information.

Warm-Up/Review:

Find the axis of symmetry for the graph y = 3x2 + 6x + 4

a. y = -1 b. x = 1 c. x = -1 d. y = 1

A graph of a quadratic function has x intercepts of (3,0) and (-7,0). Which of the following could match the graph?

a. x2 + 4x - 21 = 0 b. x2 - 10x - 21 = 0 c. x2 + 10x + 21 = 0 d. x2 - 4x + 21 = 0

Warm-Up/Review:

Warm-Up/Review:

Warm-Up/Review:(3)

Warm-Up/Review:

Why or why not?

Why or why not?

Warm-Up/Review:

Holt Algebra 1

9-3 Graphing Quadratic Functions

Write down the steps, in order, that you would follow to solve the equation

y + 6x = x2 + 9

Step 2:

The axis of symmetry is x = 3.

= 3

y = x2 – 6x + 9Rewrite in standard form.Step 1

Find the axis of symmetry.

Holt Algebra 1

9-3 Graphing Quadratic Functions

Step 3:

= 9 – 18 + 9

= 0

The vertex is (3, 0).

The y-coordinate is 0. .

y = x2 – 6x + 9

y = 32 – 6(3) + 9

Find the vertex.

Holt Algebra 1

9-3 Graphing Quadratic Functions

Step 4:

y = x2 – 6x + 9

y = x2 – 6x + 9

The y-intercept is 9; the graph passes through (0, 9).

Identify c.

Find the y-intercept.

Holt Algebra 1

9-3 Graphing Quadratic Functions

Step 5:

Since the axis of symmetry is x = 3, choose x-values less than 3. Let x = 2 y = 1(2)2 – 6(2) + 9 = 4 – 12 + 9 = 1

Let x = 1 y = 1(1)2 – 6(1) + 9 = 1 – 6 + 9 = 4

Two other points are (2, 1) and (1, 4).

Find two more points on the same side of the axis of symmetry as the point containing the y- intercept.

Holt Algebra 1

9-3 Graphing Quadratic Functions

Step 6:

Reflect the points across the axis of symmetry. Connect the points with a smooth curve.

y = x2 – 6x + 9

x = 3

(3, 0)

(0, 9)

(2, 1)

(1, 4)

(0, 9)

(1, 4)

(2, 1)

x = 3

(3, 0)

Graph the axis of symmetry, the vertex, the point containing the y-intercept, and two other points.

Step 7:

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.

*The next question will give you honest feedback about your recent focus, attention, and work habits. At this point, we shouldall be able to answer it. Write, do not say the answer, please.

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.

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)

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 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.

Holt Algebra 1

9-3 Graphing Quadratic Functions

The vertex is the highest or lowest point on a parabola. Therefore, it always represents the maximum height of an object following a parabolic path.

Remember!

Friday’s Class Work...Plus the following

Holt Algebra 1

9-3 Graphing Quadratic Functions

Holt Algebra 1

9-3 Graphing Quadratic Functions