Algebra II Parabola Quiz
1. Find the equation of the parabola through the points (-1, 17) , (1, 17) , (2, 8). Use y = ax2 + bx + c
and set up three equations, the representative matrices, and solve with inverses for full credit.
2. Find a quadratic model for the data. Use 1974 as year 0 and please watch your years.
Price of First Class Stamp
Year
1974
1978
1981
1983
1988
1995
2001
2002
Price
10
15
18
20
25
32
34
37
a) Y =
b) Describe a reasonable domain and range for this situation. Domain is x values, range y values.
c) Estimate when the first class postage was 29 cents.
(Think about where years and money would intersect on the calculator.
d) Use the model to predict when first class postage will be 50 cents. Explain why this may or may
not be valid.
3. Identify all the important points BY HAND and graph the parabolas.
f(x) = x2 + 4x + 1
y-int ______
line of symmetry
vertex ______
additional couple points
f(x) = -3x2 – 12x + 10
y-int ______
line of symmetry
vertex ______
additional couple points
4. Find a pair of numbers with a difference of 15 and a product that is a minimum.
5. For a model rocket, the altitude h, in meters as a function of time, t, is given by h = 68t – 4.9t2.
a) Find the max height of the rocket by hand.
b) How long does it take to reach that height?
6. A parabola goes through the point (2, 11) and has a vertex of (1, 5)
a) Give me the equation in vertex form y = a(x – h)2 + k
b) Give me the equation in standard form y = ax2 + bx + c
7) A parabola goes through the vertex (3, 6) and has a y-intercept of 2.
a) Give me the equation in vertex form y = a(x – h)2 + k