HONORS – CHAPTER 2 REVIEW
Name____________________________ Per______
1. DO NOT USE A CALCULATOR FOR THE FOLLOWING PROBLEMS UNLESS DIRECTED TO DO SO. 10
a. The function below is in _________________________ form. Without changing its form, graph it by first finding its vertex and then using a H-chart..
f (x) = −5(x + 4)2 + 10 5
_______________ axis of symmetry _______________ vertex
–10
–5
5
10
5
10
5
10
_______________ max/min value of the function –5
–10 20
b. The function below is in _____________________________form. Without changing its form, graph the function.
f (x) = −2(x − 1)(x + 4)
10
_______________ x-intercepts _______________ axis of symmetry
–10
–5
_______________ vertex –10
_______________ max/min value of the function
c. The function below is in _______________________ form.
–20
Without changing its form, graph it by using the method that uses TRANSFORMATIONS.
10
2
⎛1 ⎞ f (x) = − ⎜ x ⎟ − 2 ⎝3 ⎠
5 ____________________________________________________ PARENT FUNCTION
_____________________________________________________ TY P E O F T R A N S F O R M A T I O N
_____________________________________________________ TY P E O F T R A N S F O R M A T I O N
_____________________________________________________ TY P E O F T R A N S F O R M A T I O N
–10
–5
_______________ axis of symmetry _______________ vertex
–5
_______________ max/min value of the function –10
d. The function below is in _____________________________form. Without changing its form, graph the function.
f (x) =
1 2 x − 4x − 1 2
_______________ _______________ _______________ axis of symmetry vertex max/min value of the function 10
5
–5
–10
5
10
–5
–10
2. Without changing its form, state the vertex, the axis of symmetry, and the maximum/minimum value of the graph of
_________________ _________________ _______________________ axis of symmetry
f (x) = 2(x − 3) − 9 . 2
vertex
maximum / minimum value (Circle the type of value.)
3. Write a rule for h(x) given the following transformations to the graph of the function, f (x) = (x + 2)2 . Use functional notation in the process and show all steps. a. Let the graph of h(x) be a horizontal shrink by a factor of 1/5 followed with a translation 6 units right of the graph of f(x).
b. Now let the graph of h(x) be a translation of 6 units right followed with a horizontal shrink by a factor of 1/5 of f(x).
4. Determine whether the function that models each data is linear or quadratic without using a calculator. Show your work. a.
x
1
2
3
4
5
y
39
60
75
84
87
b.
x
-2
2
6
10
14
y
-15
-1
13
27
41
5. Can finite differences be used to determine what type of function is represented by the data below? If not, explain why. If so, find the type of function represented by the data. Show all work.
x
0
2
4
8
20
y
-8
-5
-2
1
4
USE A GRAPHING CALCULATOR for the next problem. Time, x 0 2.4 4.8 6. A basketball is thrown up in the air toward the hoop. The table Basketball height, y 6 14 10 shows the heights y (in feet) of the basketball after x seconds. a. What are 2 ways that you can use your calculator to determine whether to use a linear function or quadratic function? Do both of these. Explain how each method helped or did not help you make your decision.
b. Write the equation of the function that best fits the data. Round your answer to the nearest hundredth.
c. How high was the ball when the player released it?
d. What is the maximum height that the ball reaches on its path towards the basket?
e. Find the height of the basketball after 3 seconds.
f. Find the height of the basketball after 7 seconds.
Round your answer to the nearest tenth.
Round your answer to the nearest tenth.
Explain your answer.
g. Thinking about the answers for parts e and f, explain the difference between interpolation and extrapolation.
7. a. What is the coefficient of determination and describe how and why it is used.
b. State the differences between a coefficient of determination and a correlation coefficient.
8. USE YOUR GRAPHING CALCULATOR in order to find the vertex of the function f (x) = −.75x 2 + 52x − 12 . (Round to 2 decimal places.) Is the vertex a maximum or minimum point? Why?
9. A parabola has an axis of symmetry x = − 2 and passes through the point (−5,6) . Find another point that lies on the graph of the parabola. Show how you got your answer.
10. The graph shows the area y (in square feet) of rectangles that have a perimeter of 200 feet and a length of x feet.
a. Interpret the meaning of the vertex.
b. Write an equation for the parabola in intercept form. (No calculator)
c. Use the function in order to predict the area of the rectangle when the length is 2 feet. (Use a basic calculator.)
10
11. Write a quadratic function in vertex form for the parabola shown.
5
–10
–5
5
–5
–10
12. Write a quadratic function in intercept form for the parabola that passes through (4,−6) , (8,0) , and (−3,0) .
13. a. Write a quadratic function in standard form for the parabola with goes through the following points. (No calculator.) (2,7) (5,4), (3,2) Do this on a separate piece of paper. b. Then check your answer using a graphing calculator.
10
