10.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Graph y = ax 2...
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Transcript of 10.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Graph y = ax 2...
![Page 1: 10.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Graph y = ax 2 + bx + c.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd144d/html5/thumbnails/1.jpg)
10.2
Warm UpWarm Up
Lesson QuizLesson Quiz
Lesson PresentationLesson Presentation
Graph y = ax2 + bx + c
![Page 2: 10.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Graph y = ax 2 + bx + c.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd144d/html5/thumbnails/2.jpg)
10.2 Warm-Up
Evaluate the expression.
1. x2 – 2 when x = 3
2. 2x2 + 9 when x = 2
ANSWER 7
ANSWER 17
ANSWER 6.25 in.2
Martin is replacing a square patch of counter top. The area of the patch is represented by A = s2. What is the area of the patch if the side length is 2.5 inches?
3.
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10.2 Example 1
Consider the function y = –2x2 + 12x – 7.
a. Find the axis of symmetry of the graph of the function.
b. Find the vertex of the graph of the function.
SOLUTION
122(– 2)x = – b
2a= = 3 Substitute –2 for a and 12 for b.
Then simplify.
For the function y = –2x2 + 12x – 7, a = 2 and b = 12.a.
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10.2 Example 1
b. The x-coordinate of the vertex is , or 3. b 2a
–
y = –2(3)2 + 12(3) – 7 = 11 Substitute 3 for x. Then simplify.
ANSWER The vertex is (3, 11).
![Page 5: 10.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Graph y = ax 2 + bx + c.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd144d/html5/thumbnails/5.jpg)
10.2 Guided Practice
1. Find the axis of symmetry and vertex of the graph of the function y = x2 – 2x – 3.
ANSWER x = 1, (1, –4).
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10.2 Example 2
Graph y = 3x2 – 6x + 2.
Determine whether the parabola opens up or down. Because a > 0, the parabola opens up.
STEP 1
STEP 2 =Find and draw the axis of symmetry: x = – b
2a– – 62(3)= 1.
STEP 3Find and plot the vertex.
To find the y-coordinate, substitute 1 for x in the function and simplify. y = 3(1)2 – 6(1) + 2 = – 1
So, the vertex is (1, – 1).
The x-coordinate of the vertex is b2a
, or 1.–
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10.2 Example 2
STEP 4Plot two points. Choose two x-values less than the x-coordinate of the vertex. Then find the corresponding y-values.
STEP 5
Reflect the points plotted in Step 4 in the axis of symmetry.
STEP 6
Draw a parabola through the plotted points.
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10.2 Guided Practice
2. Graph the function y = 3x2 + 12x – 1. Label the vertex and axis of symmetry.
ANSWER
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10.2 Example 3
Tell whether the function f(x) = – 3x2 – 12x + 10 has aminimum value or a maximum value. Then find theminimum or maximum value.
SOLUTION
Because a = – 3 and – 3 < 0, the parabola opens down andthe function has a maximum value. To find the maximumvalue, find the vertex.
x = – = – = – 2 b2a
– 122(– 3)
f(–2) = – 3(–2)2 – 12(–2) + 10 = 22 Substitute –2 for x. Thensimplify.
The x-coordinate is – b2a
ANSWER
The maximum value of the function is f(– 2) = 22.
![Page 10: 10.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Graph y = ax 2 + bx + c.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd144d/html5/thumbnails/10.jpg)
10.2 Guided Practice
3. Tell whether the function f(x) = 6x2 + 18x + 13 has aminimum value or a maximum value. Then find theminimum or maximum value.
1 2
Minimum value;
ANSWER
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10.2 Example 4
The suspension cables between the two towers of the Mackinac Bridge in Michigan form a parabola that can be modeled by the graph of y = 0.000097x2 – 0.37x + 549 where x and y are measured in feet. What is the height of the cable above the water at its lowest point?
SUSPENSION BRIDGES
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10.2 Example 4
SOLUTION
The lowest point of the cable is at the vertex of theparabola. Find the x-coordinate of the vertex. Use a = 0.000097 and b = – 0.37.
x = – = – ≈ 1910 b2a
– 0.372(0.000097)
Use a calculator.
Substitute 1910 for x in the equation to find they-coordinate of the vertex.
y ≈ 0.000097(1910)2 – 0.37(1910) + 549 ≈ 196
ANSWER
The cable is about 196 feet above the water at its lowest point.
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10.2 Guided Practice
SUSPENSION BRIDGES
4. The cables between the two towers of the Takoma Narrows Bridge form a parabola that can be modeled by the graph of the equation y = 0.00014x2 – 0.4x + 507 where x and y are measured in feet. What is the height of the cable above the water at its lowest point? Round your answer to the nearest foot.
ANSWER
221 feet
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10.2 Lesson Quiz
1. Find the axis of symmetry and the vertex of the graph of the function y = – 4x2 + 8x – 9
2. Graph y = –2x2 + 4x + 1
ANSWER x = 1; (1, – 5)
ANSWER
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10.2 Lesson Quiz
3. An arch to the entrance of the library can be modeled by y = – 0.13x2 + 2.5x, where x and y are measured in feet. To the nearest foot, what is the height of the highest point of the arch?
ANSWER 12 ft