1. Chapter 6.2 Solving Quadratic Functions by Graphing Standard & Honors
Algebra II Mr. Gilbert
Chapter 6.2
Solving Quadratic Functions by Graphing
Standard & Honors
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2. Agenda
Warm up
Homework
Check your answers
Applet
Lesson
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3. Click the mouse button or press the Space Bar to display the answers.
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Click the mouse button or press the Space Bar to display the answers.
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5. Solving Quadratic Functions by Graphing
Example 1 Two Real Solutions (4)
Example 2 One Real Solution (3)
Example 3 No Real Solution (4)
Example 4 Estimate Roots (3)
Example 5 Write and Solve an Equation (5)
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Lesson 2 Contents

6. x –1 1 2 3 4 f (x) –4 –6 Solve by graphing.
Graph the related quadratic function
The equation of the axis of symmetry is
Make a table using x values around
Then graph each point. x –1 1 2 3 4
f (x) –4 –6
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Example 2-1a

7. Answer: The solutions of the equation are –1 and 4.
From the table and the graph, we can see that the zeroes of the function are –1 and 4.
Answer: The solutions of the equation are –1 and 4.
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Example 2-1a

8. Check Check the solutions by substituting each solution into the original equation to see if it is satisfied.
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Example 2-1a

9. Solve by graphing.
Answer:
–3 and 1
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Example 2-1b

10. Write the equation in form.
Solve by graphing.
Write the equation in form.
Add 4 to each side.
Graph the related quadratic function
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Example 2-2a

11. Notice that the graph has only one x-intercept, 2.
Answer: The equation’s only solution is 2.
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Example 2-2a

12. Solve by graphing.
Answer: 3
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Example 2-2b

13. Explore Let one of the numbers. Then
Number Theory Find two real numbers whose sum is 4 and whose product is 5 or show that no such numbers exist.
Explore Let one of the numbers. Then
Plan Since the product of the two numbers is 5, you know that
Original equation
Distributive Property
Add x2 and subtract 4x from each side.
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Example 2-3a

14. Solve You can solve by graphing the related function .
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Example 2-3a

15. Examine Try finding the product of several numbers whose sum is 4.
Notice that the graph has no x-intercepts. This means that the original equation has no real solution.
Answer: It is not possible for two numbers to have a sum of 4 and a product of 5.
Examine Try finding the product of several numbers whose sum is 4.
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Example 2-3a

16. Answer: no such numbers exist
Number Theory Find two real numbers whose sum is 7 and whose product is 14 or show that no such numbers exist.
Answer: no such numbers exist
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Example 2-3b

17. The equation of the axis of symmetry of the related function is
Solve by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.
The equation of the axis of symmetry of the related
function is
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Example 2-4a

18. The x-intercepts of the graph are between 0 and 1 and between 5 and 6.
Answer: One solution is between 0 and 1 and the other is between 5 and 6.
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Example 2-4a

19. Answer: between 0 and 1 and between 3 and 4
Solve by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.
Answer: between 0 and 1 and between 3 and 4
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Example 2-4b

20. We need to find t when and
Royal Gorge Bridge The highest bridge in the United States is the Royal Gorge Bridge in Colorado. The deck of the bridge is 1053 feet above the river below. Suppose a marble is dropped over the railing from a height of 3 feet above the bridge deck. How long will it take the marble to reach the surface of the water, assuming there is no air resistance? Use the formula where t is the time in seconds and h0 is the initial height above the water in feet.
We need to find t when and
Original equation
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Example 2-5a

21. Then locate a right bound and press twice.
Graph the related function using a graphing calculator. Adjust your window so that the x-intercepts are visible.
Use the zero feature, [CALC], to find the positive zero of the function, since time cannot be negative. Use the arrow keys to locate a left bound for the zero and press
2nd
ENTER
Then locate a right bound and press twice.
ENTER
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Example 2-5a

22. Answer:. The positive zero of the function is approximately 8
Answer: The positive zero of the function is approximately 8. It should take about 8 seconds for the marble to reach the surface of the water.
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Example 2-5a

23. Hoover Dam One of the largest dams in the United States is the Hoover Dam on the Colorado River, which was built during the Great Depression. The dam is feet tall. Suppose a marble is dropped over the railing from a height of 6 feet above the top of the dam. How long will it take the marble to reach the surface of the water, assuming there is no air resistance? Use the formula where t is the time in seconds and h0 is the initial height above the water in feet.
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Example 2-5b

24. Answer: about 7 seconds
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Example 2-5b

25. Homework Review
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26. Homework - Honors See Syllabus 6.2
pp : (multiples of 3), 38-47
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27. Homework See Syllabus 6.2 pp. 297 – 299 14-19,20-36 even,38-46
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