Math 2
EOCT Quadratic Review Homework
1) This graph represents a quadratic function.
a. Identify the location of the vertex.
b. Write an equation to represent the axis of symmetry.
c. Describe the horizontal and vertical shifts and the vertical
stretch or shrink that could be applied to the graph of y = x2 to
get this graph.
d. Write an equation in the form y  a( x  h)2  k to represent
this function.
e. What are the zeros and the y-intercept of the function?
f. What are the domain and range of the function?
g. On what interval or intervals is the function increasing? On what interval or intervals is the function
decreasing? For each interval, state whether the rate of increase or decrease is increasing or decreasing.
2. Philip is standing on a rock ledge that juts out over a lake. He tosses a rock straight up with a velocity
of 48 feet per second. The rock leaves his hand at a point 64 feet above the surface of the lake. The rock
travels upward and then falls into the lake.
This graph and table represent the height above the water, h(t), as a function of the time, t, in seconds
after Philip releases the rock.
a. What is the maximum height the rock reaches above the surface of the lake?
b. After how many seconds does the rock hit the surface of the lake?
c. Identify the vertex and the axis of symmetry of the graph.
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Math 2
EOCT Quadratic Review Homework
d. What does the y-intercept of the graph represent in this context? What does the x-intercept represent?
e. For approximately how many seconds is the rock at least 80 feet above the surface of the lake?
f. Write a function in the form h(t )  a( x  h)2  k that is represented by the graph.
g. In this problem, what are the domain and range of h(t)?
h. Write the function from part f in standard h(t )  ax 2  bx  c form.
MULTIPLE CHOICE PRACTICE:
3) The quadratic function f (x) has these characteristics:
- The vertex is located at (8, −2).
- The range is −2≤ f (x)<∞.
Which function could be f (x)?
1
a) f ( x)  x 2  8 x  30
2
1
b) f ( x)  x 2  8 x  31
2
1
c) f ( x)  x 2  8 x  34
2
1
d) f ( x)  x 2  2 x  6
2
4) The vertex of the quadratic function g(x) is located at (4, 2). An x-intercept of g(x) is located at (5, 0).
What is the y-intercept of g(x)?
a) (0,−30)
b) (0,−14)
c) (0,−4)
d) (0, 3)
1
5) What are the solutions to the equation 289  ( x  8) 2 ?
3
a) x = -27
b) x = 75
c) x = -27 and 75
d) x = -75 and 75
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Math 2
EOCT Quadratic Review Homework
6) Use the graph of the function to answer the following question.
Which statement is true about the real solutions of g(x)?
a) g(x) has no real solutions.
b) g(x) has exactly one real solution.
c) g(x) has 2 real solutions that are rational.
d) g(x) has 2 real solutions that are irrational.
7) Which expression is equivalent to
a)
19 22
 i
3 3
b)
29 2
 i
3 3
c)
19 22
 i
5 5
d)
29 2
 i
5 5
12  5i
?
2i
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