Name: _______________________
Alg CHAPTER 9 TEST REVIEW
1) Order each group of quadratic function from widest to narrowest graph:
𝟏
i.) a.) y = 3x2, b.) y = -2x2, c.)y = -4x2
𝟐
ii) a.)y = 𝟓x2, b.) y = –9x2, c.) y = – 𝟑x2
2) Tell whether each parabola opens upward or downward and whether the vertex is maximum or
minimum.
𝟏
a) y = 6x2
b) y = –8x2
c) y = – 𝟑x2
3) Graph each quadratic function using the AOS, Vertex and Y-intercept. SHOW ALL WORK!
a) y = x2 + 6x + 1
b ) y = –2x2 + 12x + 4
c) y = x2 – 2x – 8
4) Solve each equation without the quadratic formula.
a) 2x2 – 10 = – 4
b) 4x2 + 3 = 3
c) 4x2 – 8 = 32
d) x2 + 400 = 0
e) 7x2 – 8 = 20
f) 2x2 – 1400 = 0
g) 3x2 – x2 = 10
h) 2x2 + 6 – x2 = 9
i) 6x2 – 6 = 12
5)
Use the discriminant to determine the number of real-number solutions.
a) 8x2 + 2x = 8x
6)
c) –x2 = 4x + 6
Use the quadratic formula to solve. Round to the nearest tenth, if necessary.
a) 𝒙𝟐 − 𝟐𝒙 = 𝟖
c) 𝒙𝟐 + 𝟐𝒙 + 𝟔 = 𝟎
7)
b) 4x2 = 9x – 3
b) 𝒙𝟐 = −𝟔𝒙 − 𝟗
d.) 𝟑𝒙𝟐 + 𝟏𝒙 − 𝟐 = 𝟎
Solve the following by factoring.
a) 𝒙𝟐 − 𝟒𝒙 = 𝟐𝟏
d) 𝟖𝒙𝟐 − 𝟔𝒙 = 𝟎
b) 𝟔𝒙𝟐 − 𝟏𝒙 − 𝟐 = 𝟎
e) 𝒙𝟐 − 𝟒𝒙 = 𝟐𝟏
c) 4𝒙𝟐 + 𝟐𝟎𝒙 + 𝟐𝟓 = 𝟎
A mini canon is shooting a potato into the air. The function that describes its path is 𝒚 = −𝒙𝟐 + 𝟖𝒙 + 𝟒
where y is the height in feet and x is the number of seconds. **Hint draw an sketch of the graph.
8)
a.) After how many seconds will it reach its highest point? How high will it reach?
b.)What is the height of the barrel of the cannon?
c.) How long will it take for the potato to hit the ground (aka. When will the height be 0)?
Round to the nearest tenth of a second.
Describe how each graph differs from the graph of y = x2.
9)
a)
y = 4x2 – 3
c)
y = – 𝟑x2
b) y = –x2 + 2
𝟐
𝟏
d) y = 𝟓x2 + 1
10.) Solve the following using the 4 different methods.
Method 1
Method 2
𝒙𝟐 = 𝟗
Method 3
Method 4