![Page 1: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/1.jpg)
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
![Page 2: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/2.jpg)
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
![Page 3: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/3.jpg)
Geometry
The future belongs to those who believe in the beauty of their dreams.
Eleanor Roosevelt
![Page 4: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/4.jpg)
Dividers• Purpose/Goals
• Notes
• Assignments
• Check-Ups
• Paper/Graph Paper
![Page 5: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/5.jpg)
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
![Page 6: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/6.jpg)
Solve:
2x + 5 = -9
2x2 + 3 = 35
3x2 + 2x = 35
![Page 7: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/7.jpg)
Quadratic function:
y = ax2 + bx + c, but a ≠ 0
y = 4x2 + x – 4Is this a quadratic function? If yes, find a, b, c.
![Page 8: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/8.jpg)
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).
![Page 9: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/9.jpg)
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).
![Page 10: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/10.jpg)
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).
![Page 11: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/11.jpg)
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).
![Page 12: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/12.jpg)
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).
![Page 13: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/13.jpg)
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).
![Page 14: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/14.jpg)
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).
![Page 15: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/15.jpg)
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
![Page 16: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/16.jpg)
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
![Page 17: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/17.jpg)
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!
![Page 18: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/18.jpg)
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!
![Page 19: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/19.jpg)
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!
![Page 20: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/20.jpg)
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
![Page 21: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/21.jpg)
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!
![Page 22: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/22.jpg)
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?
![Page 23: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/23.jpg)
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?
![Page 24: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/24.jpg)
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?
![Page 25: 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](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649dda5503460f94ad0b8a/html5/thumbnails/25.jpg)
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