CHAPTER 2 REVIEW
Algebra 2
Name____________________________ Per______
1. State the axis of symmetry , vertex , and minimum or maximum value of each of the functions. SHOW ALL WORK. DO NOT USE A CALCULATOR. Write any improper fractions as mixed numbers. a.
c.
1 f (x) = − x 2 − 6x + 8 2
f (x) = 4(x + 9)2 − 5
b.
f (x) = 4(x − 5)(x + 2)
_______________ axis of symmetry
_______________ axis of symmetry
_______________ vertex
_______________ vertex
_______________ max/min value of the function
_______________ max/min value of the function
_______________ axis of symmetry
d.
f (x) = x 2 + 8
_______________ axis of symmetry
_______________ vertex
_______________ vertex
_______________ max/min value of the function
_______________ max/min value of the function
2. DO NOT USE A CALCULATOR FOR THE FOLLOWING PROBLEMS UNLESS DIRECTED TO DO SO. 20
a. The function below is in _____________________________form.
Without changing its form, graph the function. (NOTE THE SCALE FOR THE Y-AXIS.) f (x) = −2(x − 1)(x + 5)
10
–10
5
–5
–10
–20
___________________ __________________________ axis of symmetry vertex
___________________ __________________________ max / min value of x-intercepts the function
10
b. The function below is in _____________________________form.
Without changing its form, graph the function. f (x) = 2x 2 − 12x + 10
________________ ______________ ______________ axis of symmetry vertex max or min value of f(x) 10
5
–10
–5
5
10
–5
–10
c. The function below is in _______________________ form.
Without changing its form, graph it by using the method that uses TRANSFORMATIONS. List the transformations in the order that they should be used. 2
⎛1 ⎞ f (x) = − ⎜ x ⎟ − 5 ⎝2 ⎠
10
5 ____________________________________________________ PARENT FUNCTION –10 _____________________________________________________ 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
–5
5
_______________ axis of symmetry _______________ vertex
–5
_______________ max/min value of the function –10
10
3. Write a rule for h(x) given the following transformations to the graph of the function, f (x) = x 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 of f(x).
b. Let the graph of h(x) be a translation of 6 units left followed with a reflection across the x-axis of f(x).
USE A GRAPHING CALCULATOR for the next problem. Time, x 0 2.4 4.8 4. 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. Explain your answer.
Round your answer to the nearest tenth.
g. Thinking about the answers for parts e and f, explain the difference between interpolation and extrapolation.
5. Determine whether the function that models the set of data is linear or quadratic. Use your graphing calculator in order to write the equation of the function. Give two reasons why you are sure that you chose the best type of function. x
-2
2
6
10
14
y
-15
-1
13
27
41
6. 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?
7. 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.
8. Write the x-intercepts of the function f (x) = −(x + 6)(x − 3) as ordered pairs.
9. 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. Write an equation for the parabola in intercept form without using a calculator.
b. Use the function in order to predict the area of the rectangle when the length is 2 feet. Show work.
c. Interpret the meaning of the vertex in this situation.
y 10
10. Write a quadratic function in vertex form for the parabola shown. (No calculator)
5 (2,3) –10
5
–5
(-1, -4)
10
–5
–10
11. Write a quadratic function in intercept form for the parabola that passes through (2,20) , (8,0) , and (−3,0) . (No calculator)
12. a. Write a quadratic function in standard form for the parabola with goes through the following points: (3,-9), (2,1), (-5,15) . Do this on a separate piece of paper. DO NOT USE YOUR GRAPHING CALCULATOR. b. When you are finished, check your equation by entering the data into your calculator and using quadratic regression.
x
CHAPTER 2
V O C A B U L A R Y
Name ___________________________________ Per______
Fill in the blanks with the appropriate vocabulary from chapter 2.
1. A line that divides a parabola into mirror images and passes through the vertex is called the __________________________________________________.
2. A function written as f (x) = a(x − p)(x − q) , where a ≠ 0 is written in __________________________________________________.
3. The y-coordinate of the vertex of the function f (x) = ax 2 + bx + c when a > 0 is called the ________________________________________________________. 4. A function that has a degree of 2 is called a _____________________________________ function. 5. The graph of a quadratic function is called a ___________________________________.
6. A function written as f (x) = a(x − h)2 + k , where a ≠ 0 is written in _____________________________________________________. 7. The lowest point on a parabola that opens up or the highest point on a parabola that opens down is called a ______________________________.
8. The function f (x) = −2x 2 + 7x − 8 is an example of a ______________________________________ function. 9. The y-coordinate of the vertex of the function f (x) = ax 2 + bx + c when a < 0 is called the
__________________________________________________________. 10. A function written as f (x) = ax 2 + bx + c , where a ≠ 0 is written in _________________________________________________. 11. In the above definition of a quadratic function, explain why is a not able to be equal to 0? ______________________________________________________________________________________ ______________________________________________________________________________________ 12. The _______________________________________________________ shows how well an equation fits a set of data and whether the function can be used to predict y values. It is represented by the symbol ______. It is a number from _______ to _______. The closer the number is to _______, the better the fit.
