Algebra II Core Worksheet for Understanding 1st half of Ch 4
Name _________________
Graph each function:
1.
y = 2|x – 3| + 1
4. y = 2(x – 3)2 + 1
7. Given y = x2 – 8x + 19,
a) find the vertex
2. y = -3|x + 2|
3. y = ½ |x – 1| - 3
5. y = -2(x + 5)2 – 1
6. y = x2 + 5
8. Given y = -2x2 – 4x + 6,
a) find the vertex
b) write in vertex form:
b) write in vertex form:
c) does it have a max or min?
c) does it have a max or min?
d) State the domain
d) State the domain
e) State the range
e) State the range
f) State the axis of symmetry
f) State the axis of symmetry
Find the quadratic equation of the parabola passing through the following points:
9. (2, -8), (3, -8), (6, 4)
10. (-1, -12), (0, -6), (3, 0)
Factor completely:
11.
x2 + 11x + 28
12,
x2 – 8x – 20
13.
x2 – 7x + 12
14.
16x2 + 12x
15.
9x2 – 15x
16.
9x2 – 16
17.
25x2 – 81
18.
3x2 + 10x + 8
19.
5x2 – 17x + 6
20.
2x2 – 10x + 12
Algebra II Last Problem of Test Core Alg II – Group Part
Name ___________________
Work with your group of 2 students. You can work with your group on this problem, using your graphing
calculator. If you can’t work with your group – work by yourself. You cannot go to another group and ask
what they got for an answer. EVERYONE in your group fills out an answer key with explanations on how to
get the answer!!!
Given: A certain cannon is fired from a spot above the ground, at a certain angle, the height of the cannonball
above the ground, h, in meters, at a time, t, in seconds, is found by the function h(t) = -4.9t2 + 27.5t + 8.6.
a) Draw a sketch of this problem with your axis’s numbered and labeled:
b) What was the initial height of the cannon? _______
E. C. How do you know, looking at the equation?
c) What is the maximum height of the cannonball and how long did it take to get there? (Round to
hundreths)
Height _______
How long did it take _________
E. C. What important part of the graph is this? (Use math word)
d) How long did it take the cannon to hit the ground? _________
E. C. What important part of the graph is this and why would it be this part of the graph?
e) How high in the air was the cannonball after 0.5 seconds? ____________
f) When will the cannon first be 40 m. in the air? ____________