10 - Loudoun County Public Schools
10.3 Solving Quadratic Equations by Graphing
******IMPORTANT******REMEMBER*******IMPORTANT******REMEMBER*******
The solution to any equation can be called any of the following:
__________________, ___________________, __________________, ___________________
To solve a quadratic equation by graphing all you need to do is:
1. __________________ 2. __________________ 3. __________________
A Quadratic Equation can have 3 types of solutions.
Two Solutions One Solutions No Solutions
Example:
1. [pic]
2. [pic]
Solving Quadratic Equations by Graphing on the Calculator
|Solve: [pic] |Standard 10 x 10 window |
|Since this equation is set equal to zero, the roots will be the locations where the graph crosses the |[pic] |
|x-axis (if the roots are real numbers). | |
|(Remember that the x-axis is really just y = 0.) | |
| |[pic] |
|1. Set [pic] |[pic] |
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|2. Use the ZERO command to find the roots -- 2nd TRACE (CALC), #2 zero | |
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|3. Left bound? Move the spider as close to the root (where the graph crosses the x-axis) as possible. | |
|Hit the left arrow to move to the "left" of the root. Hit ENTER. A "marker" ► will be set to the left | |
|of the root. | |
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|4. Right bound? Move the spider as close to the root (where the graph crosses the x-axis) as possible. | |
|Hit the right arrow to move to the "right" of the root. Hit ENTER. A "marker" ◄ will be set to the | |
|right of the root. | |
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|5. Guess? Just hit ENTER. | |
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|6. Repeat the entire process to find the second root | |
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|Answer: | |
|One of the roots is x = -2 | |
|When you repeat the above steps the other root is x = 7 | |
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|So, the answer to the quadratic equation is –2 and 7 | |
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Practice: Solve the Following Equations by Graphing.
|1. [pic] |2. [pic] |
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|3. [pic] |4. [pic] |
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|5. [pic] |6. |
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Out the Door Activity. This must be turned in prior to leaving the class! Name:
(Work Must be Shown to receive credit!) _____ __________
1. 2.
3. 4.
5. 6.
7. 8.
10.3 Homework: Solve the Quadratic Equation. For #1-6 you should use the calculator to graph and find the solution. For #7-10 you should graph by hand and find the solution.
|1. [pic] |2. [pic] |
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|Solution(s): _______________________ |Zero(s): __________________________ |
|3. [pic] |4. [pic] |
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|X-Intercept(s): ____________________ |Root(s): __________________________ |
|5. [pic] |6. [pic] |
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|Zero(s): _________________________ |Solution(s): _______________________ |
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|7. [pic] |
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|Vertex: X-Intercepts: |
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|8. [pic] |
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|Vertex: Solutions: |
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|9. [pic] |
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|Vertex: Zeros: |
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|10. [pic] |
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|Vertex: Solutions: |
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-----------------------
133
y
x
10
10
-10
-10
[pic]
x2 – 4 = 0
Which is the solution set for the equation above?
F {-4, 1}
G {-2, 2}
H {-1, 4}
J {0, 4}
Which is a zero of the function f(x) = x2 + 3x – 4?
A -4
B -1
C 3
D 4
Which is the solution set for x2 – 5x – 14 = 0?
F {-7, -2}
G {-7, 2}
H {-2, 7}
J {2, 7}
What are the solutions to the equation below?
[pic][pic]x2 – 12 = 0
A x = -4 or x = 4
B x = -12 or x = 9
C x = -3 or x = 3
D x = 3 or x = 9
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