algebra t3 today: 9.3 check up 9.4 instruction break finish 9.4 practice all dreams can come true....
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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