Graphing Quadratic Functions (Parabolas)

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Show your work for each problem.

1.
For the function , what is the value of coefficient ?
1. a)
2. b)
3. c)
4. d)
2.
A parabola with will:
1. a)Open upward and have a maximum
2. b)Open downward and have a minimum
3. c)Open downward and have a maximum
4. d)Open upward and have a minimum
3.
What is the y-intercept of ?
4.
Find the axis of symmetry for . Give your answer as
5.
The discriminant of is:
1. a) (two real roots)
2. b) (one real root)
3. c) (two real roots)
4. d) (no real roots)
6.
Find the vertex of .
7.
Find the x-intercepts of .
8.
The parabola has a maximum or minimum value? What is that value?
9.
Which parabola is narrower (steeper)?
1. a)
2. b)
3. c)
4. d)
10.
Graph by finding the vertex, y-intercept, and x-intercepts.
11.
A ball is thrown upward with height meters after seconds. What is the maximum height reached?
12.
Analyze : find direction, vertex, axis of symmetry, y-intercept, and x-intercepts.
13.
A company's revenue is modeled by where is the price in euros. What price maximizes revenue?
1. a)25 euros
2. b)20 euros
3. c)10 euros
4. d)50 euros
14.
Use the discriminant to determine how many x-intercepts has, then explain what this means for the graph.
15.
For , what is the minimum value of the function?
16.
Find all key features of : vertex, axis of symmetry, y-intercept, and x-intercepts.