4-2 Solving Quadratic Equations by Graphing CCSS PRECISION Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located. 5. SOLUTION: Graph the related function
.
The x-intercepts of the graph indicate that the solutions are –3 and 6.
7.
SOLUTION: Graph the related function
The x-intercepts of the graph indicate that one solution is between –2 and –1, and the other solution is 3.
9.
SOLUTION:
Graph the related function
.
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The x-intercepts of the graph indicate that one solution is between –2 and –1, and the other solution is 3. 4-2 Solving Quadratic Equations by Graphing
9.
SOLUTION:
Graph the related function
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The graph has no x-intercepts. Thus, the equation has no real solution.
11.
SOLUTION:
Graph the related function
.
The x-intercepts of the graph indicate that one solution is between –5 and –4, and the other solution is between 5 and 6.
13. PHYSICS How long will it take an object to fall from the roof of a building 400 feet above ground? Use the formula , where t is the time in seconds and the initial height h 0 is in feet. eSolutions Manual - Powered by Cognero
SOLUTION:
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The x-intercepts of the graph indicate that one solution is between –5 and –4, and the other solution is between 5 and 6. 4-2 Solving Quadratic Equations by Graphing
13. PHYSICS How long will it take an object to fall from the roof of a building 400 feet above ground? Use the formula , where t is the time in seconds and the initial height h 0 is in feet.
SOLUTION: Solve the equation
It will take 5 seconds for an object to fall.
Use the related graph of each equation to determine its solutions.
15.
SOLUTION: The graph has no x-intercepts. Thus, the equation has no real solution. 17.
SOLUTION: The x-intercept of the graph is –2. Thus, the solution of the equation is –2.
19.
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SOLUTION: The x-intercept of the graph is –2. Thus, the solution of the equation is –2. 4-2 Solving Quadratic Equations by Graphing
19.
SOLUTION: The x-intercepts of the graph are –3 and 4. Thus, the solutions of the equation are –3 and 4.
Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.
21.
SOLUTION: Graph the related function .
The x-intercepts of the graph indicate that the solutions are –2 and 0.
23.
SOLUTION: Graph the related function
.
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The x-intercepts of the graph indicate that the solutions are –4 and 6.
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The x-intercepts of the graph indicate that the solutions are –2 and 0. 4-2 Solving Quadratic Equations by Graphing 23.
SOLUTION: Graph the related function
.
The x-intercepts of the graph indicate that the solutions are –4 and 6.
25.
SOLUTION:
Graph the related function
.
The graph has no x-intercepts. Thus, the equation has no real solution.
27.
SOLUTION:
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Graph the equation
.
The graph has no x-intercepts. the equation has no real solution. 4-2 Solving Quadratic Equations Thus, by Graphing
27.
SOLUTION:
Graph the equation
.
The x-intercepts of the graph indicate that one solution is between 1 and 2, and the other solution is between –1 and 0.
29.
SOLUTION:
Graph the related function
.
The graph has no x-intercepts. Thus, the equation has no real solution.
Use the tables to determine the location of the zeros of each quadratic function.
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The graph has no x-intercepts. the equation has no real solution. 4-2 Solving Quadratic Equations Thus, by Graphing
Use the tables to determine the location of the zeros of each quadratic function.
31. SOLUTION: In the table, the function value changes from positive to negative between 0 and 1. So, one solution is between 0 and 1. Similarly, the function value changes from negative to positive between 2 and 3. So, the other solution is between 2 and 3. NUMBER THEORY Use a quadratic equation to find two real numbers that satisfy each situation, or show that no such numbers exist.
33. Their sum is –15, and their product is –54. SOLUTION: Let x represent one of the numbers. Then −15 – x is the other number.
Solve the equation
.
The two numbers are 3 and –18. 35. Their sum is 12, and their product is –84.
SOLUTION: Let x represent one of the numbers. Then 12 − x is the other number.
Solve the equation
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The two numbers are about –5 and about 17.
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4-2 Solving Equations by Graphing The twoQuadratic numbers are 3 and –18. 35. Their sum is 12, and their product is –84.
SOLUTION: Let x represent one of the numbers. Then 12 − x is the other number.
Solve the equation
The two numbers are about –5 and about 17.
37. Their sum is –8 and their product is –209.
SOLUTION: Let x represent one of the numbers. Then –8 − x is the other number.
Solve the equation
The two real numbers are 11 and –19.
Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.
41.
SOLUTION: eSolutions Manual - Powered by Cognero Graph the related function
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.
The twoQuadratic real numbers are 11 and 4-2 Solving Equations by–19. Graphing
Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.
41.
SOLUTION: Graph the related function
.
The x-intercepts of the graph indicate that one solution is –3, and the other solution is between 2 and 3.
43.
SOLUTION: Graph the related function
.
The x-intercepts of the graph indicate that one solution is between –3 and –2, and the other solution is between 1 and 2.
45.
SOLUTION: Graph the related function
.
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The x-intercepts of the graph indicate that one solution is between –3 and –2, and the other solution is between 1 and 2. 4-2 Solving Quadratic Equations by Graphing
45.
SOLUTION: Graph the related function
.
The x-intercepts of the graph indicate that one solution is between –1 and 0, and the other solution is between 4 and 5.
47.
SOLUTION: Graph the related function
.
The x-intercepts of the graph indicate that one solution is between 3 and 4, and the other solution is between 8 and 9.
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