Chapter 14 Study Guide
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1) What is the Quadratic Formula and how did we derive it?
2) What is the difference between solving a quadratic and Finding the Zeroes?
3) Solve each of the following equations by extracting the square root.
a) 𝒙𝟐 = 𝟔𝟒
b) 𝒙𝟐 + 𝟑 = 𝟏𝟑
c) (𝒙 − 𝟐)𝟐 = 𝟒𝟒
4) Find the c value that completes the square.
a) 𝒙𝟐 − 𝟏𝟎𝒙 + ________
b) 𝒙𝟐 + 𝟐𝟐𝒙 + _______
c) 𝒙𝟐 + 𝟕𝒙 + _______
5) Solve each of the following by completing the Square
a) 𝒙𝟐 + 𝟖𝒙 − 𝟐𝟎 = 𝟎
b) 𝒙𝟐 − 𝟔𝒙 − 𝟏𝟏 = 𝟎
c) 𝒙𝟐 + 𝟑𝒙 + 𝟏 = 𝟎
6) Solve each of the following using factoring (Check GCF First)
a) 𝒙𝟐 − 𝟏𝟏𝒙 − 𝟒𝟐 = 𝟎
b) 𝟑𝒙𝟐 + 𝟏𝟖𝒙 − 𝟐𝟏 = 𝟎
c) 𝟐𝒙𝟐 + 𝟏𝟏𝒙 − 𝟔 = 𝟎
7) Find the Discriminant for each quadratic and determine the number of Solutions/Zeroes
a) 𝒙𝟐 − 𝟔𝒙 − 𝟐 = 𝟎
b) 𝟓𝒙𝟐 + 𝟏𝟎𝒙 + 𝟓 = 𝟎
c) 𝟑𝒙𝟐 + 𝟐𝒙 + 𝟒 = 𝟎
8) Solve each of the following using the Quadratic Formula
a) 𝒙𝟐 − 𝟔𝒙 − 𝟐 = 𝟎
b) 𝟓𝒙𝟐 + 𝟏𝟎𝒙 + 𝟓 = 𝟎
c) 𝟑𝒙𝟐 + 𝟐𝒙 + 𝟒 = 𝟎
9) Find the Zeroes using (Use Any Method: Factor, Complete Square, Quadratic Formula)
a) 𝒙𝟐 − 𝟔𝒙 − 𝟏𝟔 = 𝟎
b) 𝒙𝟐 + 𝟖𝒙 − 𝟏 = 𝟎
c) 𝟑𝒙𝟐 − 𝟕𝒙 + 𝟔 = 𝟎
10) Find the Interval of Solutions for each Quadratic Inequality.
a) 𝒙𝟐 − 𝒙 − 𝟕 ≤ 𝟓
b) 𝒙𝟐 + 𝟏𝟒𝒙 + 𝟖 > −𝟏𝟔
c) −𝒙𝟐 + 𝟐𝒙 + 𝟑 > −𝟓
11) Find the Point(s) of intersection for each of the System of Quadratics.
𝒚 = 𝒙𝟐 − 𝟑𝒙 − 𝟏𝟖
𝒚 = 𝒙𝟐 − 𝟖𝒙 + 𝟐𝟖
a) {
b) {
𝒚=𝒙+𝟑
𝒚 = 𝟒𝒙 − 𝟖
𝒚 = 𝒙𝟐 − 𝟔𝒙 + 𝟏𝟎
c) {
𝒚 = −𝒙𝟐 + 𝟖𝒙 − 𝟏𝟎
d) {
𝒚 = 𝒙𝟐 − 𝟔𝒙 + 𝟗
𝒚 = 𝒙𝟐 − 𝟒𝒙 + 𝟑
Review Topics
12) Create an algebraic expression that fits each of the following descriptions.
a) A trinomial whose degree is 6.
b) A monomial with a coefficient of 5.
13) Simplify each of the following expressions using addition, subtraction, & multiplication.
a) (4𝑚2 + 9𝑚) − (−2𝑚2 + 6)
b) (−𝑥 2 − 12) + (4𝑥 2 − 6)
c) (2𝑥 + 1)(3𝑥 − 8)
14) Factor out the GCF
𝑚3 − 9𝑚
15) Factor using the diamond method
𝑥 2 + 6𝑥 + 8
16) Factor each using the long diamond method
a) 2𝑥 2 + 3𝑥 − 9
b) 2𝑥 2 + 11𝑥 + 5
17) Factor each Difference of Squares
a) 𝑥 2 − 9
b) 4𝑥 2 − 25𝑦 2
18) Factor the Perfect Square Trinomials
𝑥 2 − 6𝑥 + 9
19) Factor each by grouping.
2𝑝3 + 5𝑝2 + 6𝑝 + 15
20) Using each of the parabolas drawn below identify each of the key features listed.
Opens up or down
Vertex
Max/Min Point
Axis of Symmetry
Domain
Range
Zeroes
y-intercept
21) Calculate the distance between points.
(9,3) & (-2,7)
23) Solve for x
22) Solve for x.
5 − 2(𝑥 + 2) = 15