Algebra T3

Today:• 9.3 Check Up• 9.4 Instruction• Break• Finish 9.4• Practice

All Dreams can come true. If we have the courage to pursue them.

Walt Disney

Assignment

The future belongs to those who believe in the beauty of their dreams.

Eleanor Roosevelt

Due tomorrow:• 9.3 p521 #21-57

x3• Quiz 9.1-3

Monday• Supplies

Checked during Quiz

Geometry

The future belongs to those who believe in the beauty of their dreams.

Eleanor Roosevelt

Dividers• Purpose/Goals

• Notes

• Assignments

• Check-Ups

• Paper/Graph Paper

Algebra T3

9.4 Solving Quadratic Equations by Graphing

Objective:1.Solve quadratic equations by

graphing2.Solve Real World problems involving

quadratic equations

Vocabulary: zeros, roots

Solve:

2x + 5 = -9

2x2 + 3 = 35

3x2 + 2x = 35

Quadratic function:

y = ax2 + bx + c, but a ≠ 0

y = 4x2 + x – 4Is this a quadratic function? If yes, find a, b, c.

Quadratic equation in standard form:

0 = ax2 + bx + c, but a ≠ 0

0 = 4x2 + x - 4

Is this a quadratic equation? If yes, put into standard form and find a, b, c.

Hint: A quadratic equation can have only 3 kinds of terms. - x2, x, and numbers (constants).

Quadratic equation in standard form:

0 = ax2 + bx + c, but a ≠ 0

2x = 4x2 + 4

Is this a quadratic equation? If yes, put into standard form and find a, b, c.

Hint: A quadratic equation can have only 3 kinds of terms. - x2, x, and numbers (constants).

Quadratic equation in standard form:

0 = ax2 + bx + c, but a ≠ 0

0 = x2 + 4

Is this a quadratic equation? If yes, put into standard form and find a, b, c.

Hint: A quadratic equation can have only 3 kinds of terms. - x2, x, and numbers (constants).

Quadratic equation in standard form:

0 = ax2 + bx + c, but a ≠ 0

-x2 + 4x = 2x - 6

Is this a quadratic equation? If yes, put into standard form and find a, b, c.

Hint: A quadratic equation can have only 3 kinds of terms. - x2, x, and numbers (constants).

Quadratic equation in standard form:

0 = ax2 + bx + c, but a ≠ 0

4x + 2 = x – 6

Is this a quadratic equation? If yes, put into standard form and find a, b, c.

Hint: A quadratic equation can have only 3 kinds of terms. - x2, x, and numbers (constants).

Quadratic equation in standard form:

0 = ax2 + bx + c, but a ≠ 0

2x2 + 5x - 2 = 2x2 + x + 7

Is this a quadratic equation? If yes, put into standard form and find a, b, c.

Hint: A quadratic equation can have only 3 kinds of terms. - x2, x, and numbers (constants).

Quadratic equation in standard form:

0 = ax2 + bx + c, but a ≠ 0

2x2 + 5x - 2 = 25x2 + x + 7

Is this a quadratic equation? If yes, put into standard form and find a, b, c.

Hint: A quadratic equation can have only 3 kinds of terms. - x2, x, and numbers (constants).

Quadratic equation in standard form:

0 = ax2 + bx + c, but a ≠ 0

4x2 = 16

Is this a quadratic equation? If yes, put into standard form and find a, b, c.

Hint: A quadratic equation can have only 3 kinds of terms. - x2, x, and numbers (constants).

Solve it!

Graph it!

solutions = roots = zeros

Steps to graph a quadratic equation

1. Put equation into standard form

2. Replace the 0 with y

3. Graph the function by finding the x-coordinate of the vertex and other x’s in a table

4. Find the zeros – these are the solutions

5. Check answers!Graph: 4x2 = 16

Steps to graph a quadratic equation with FRIEND

1. Put equation into standard form

2. Replace the 0 with y

3. Graph the function on your calculator using the Y= button

4. Find the zeros using the calc menu ( 2nd TRACE ), setting left and right boundaries and making a guess.

5. Check answers!Graph: 4x2 = 16

Super Tip: Don’t forget to find both answers!

Steps to graph a quadratic equation with FRIEND

1. Put equation into standard form

2. Replace the 0 with y

3. Graph the function on your calculator using the Y= button

4. Find the zeros using the calc menu ( 2nd TRACE ), setting left and right boundaries and making a guess.

5. Check answers!Graph: x2 - 4x = 5

Super Tip: Don’t forget to find both answers!

Steps to graph a quadratic equation with FRIEND

1. Put equation into standard form

2. Replace the 0 with y

3. Graph the function on your calculator using the Y= button

4. Find the zeros using the calc menu ( 2nd TRACE ), setting left and right boundaries and making a guess.

5. Check answers!Graph: x2 = -x + 6

Super Tip: Don’t forget to find both answers!

Steps to graph a quadratic equation with FRIEND

1. Put equation into standard form

2. Replace the 0 with y

3. Graph the function on your calculator using the Y= button

4. Find the zeros using the calc menu ( 2nd TRACE ), setting left and right boundaries and making a guess.

5. Check answers!Graph: x2 = -x + 6

Super Tip: Don’t forget to find both answers!

12x31 2

Steps to graph a quadratic equation with FRIEND

1. Put equation into standard form

2. Replace the 0 with y

3. Graph the function on your calculator using the Y= button

4. Find the zeros using the calc menu ( 2nd TRACE ), setting left and right boundaries and making a guess.

5. Check answers!Graph: make one

up!

Super Tip: Don’t forget to find both answers!

A baseball is thrown at 100 mph ft/sec from left field toward home plate. The models below give paths of the ball for two initial angles, with height of y and horizontal distance x (both measure in feet)

6.466x.00195xy :25

6.268x.00171xy :152o

2o

If home plate is 236 feet away, which angle(s) have the ball hitting the ground before reaching the plate?

A baseball is thrown at 100 mph ft/sec from left field toward home plate. The models below give paths of the ball for two initial angles, with height of y and horizontal distance x (both measure in feet)

6.466x.00195xy :25

6.268x.00171xy :152o

2o

How high did the ball fly for each throw?

A baseball is thrown at 100 mph ft/sec from left field toward home plate. The models below give paths of the ball for two initial angles, with height of y and horizontal distance x (both measure in feet)

6.466x.00195xy :25

6.268x.00171xy :152o

2o

What angle should a ball be thrown to maximize it’s distance?

Assignment

Due tomorrow:• 9.4 529 #18-20,

21-43 odd – make sketch of graph

• Quiz 9.1-4 tomorrow

All Dreams can come true. If we have the courage to pursue them.

Walt Disney