Download yk=a(xh)2 - MICDS Intranet Menu

Algebra 2
Unit 9
Unit Test
Good Luck ________________________
28 January, 2005
Fischer
Vertex Form:
y – k = a(x – h)2
Vertex: x =
-b ± b2 - 4ac
x=
2a
-b
2a
Standard Form:
y = ax2 + bx + c
Roots (x-intercepts) Form:
y = a(x - r)(x - s)
1. Given f  x   3x2  6 x  4
a. What’s the vertex?
[6]
b. Does this parabola open up or down?
[3]
c. What’s the y-intercept?
[3]
d. Does this parabola have a maximum or a minimum? If so, where does
it occur?
[5]
e. When is this function neither increasing or decreasing?
[4]
2. Let f  x   2 x2  13x  7 . Show all your work.
a. Find f 8 and write your answer as an ordered pair.
[5]
b. Find x when f  x   13 and write your answer as an ordered pair. [8]
c. Find x when f  x   35 and write your answer as an ordered pair. [8]
3. Find the particular equation of the quadratic function containing the given
ordered pairs. Show all your work.
a. The vertex is (4, 1) and includes the point (2, 9).
[9]
b. The roots (4, 0) and (-6, 0) that includes the point (3, 27).
[9]
4. Use the discriminant to determine the type of roots the quadratic has:
either (1) Rational, (2) Irrational, (3) Complex, or (4) One double root. Show
all your work!
a. y = x2 – 18x + 81
[5]
b. y = -x2 – 10x – 12
[5]
5. The following quadratic has one x-intercept: y = 5x2 + 8x + c. Your job is to
calculate the exact value of c.
[5]
6. Given: y – 9 = 3(x – 2) 2. Answer the following questions.
a. What is the vertex?
[4]
b. Find the y-intercept.
[7]
c. Make a sketch of the graph.
[3]
d. Based on your sketch and without doing any algebra on the given
equation, determine what values the discriminant can be.
[5]
7. Given y – 12 = -3(x + 2) 2, find the x-intercepts.
[6]
Bonus
We have been studying quadratic equations; equations of the form
Y = ax2 + bx + c. Below is the graph of a cubic equation, y = ax3 + bx2 + cx + d.
Notice the cubic is raised to the third power, it has three roots! Many of the
rules of quadratics apply to cubics, however, their graphs are very different
pictures. Notice that one end goes up to positive infinity and one end goes down
to negative infinity.
1. Draw a cubic equation that has one double root, and one single root with a > 0.
2. Draw a cubic with three roots and a < 0.