Download Algebra Review Worksheet on Quadratics

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CC Algebra II
Algebra II Review Factoring & Solving Quadratics
Methods to Factor Quadratic Equations
Factoring Trinomials
Quadratic Formula
x2 + (a + b)x + (ab) 
(x + a)(x + b)
Compare to ax2 + bx + c and
substitute
Completing The Square
𝑏 2
𝑏 2
ax2 + bx + (2) = c + (2)
Now I can factor the trinomial as
explained in the first column, or
using the difference of two
squares.
What multiplies to the third term
and adds to the middle term?
I.) Match the following quadratics with their roots:
_____ x2 + 10x + 11
a. x = -11, 1
_____ x2 + 10x – 11
b. x = 3, 7
_____ x2 – 10x + 11
c. x = −5 ± √14
_____ x2 – 10x – 11
d. x = 5 ± √14
_____ (x - 5)2 = 4
e. x = 11, -1
II. Solve by Factoring
1.) x2 – 64 = 0
2.) x2 – 6x – 16 = 0
3.) x2 + 3x = 40
4.) 2 x 2  3x  1  0
5.) x² – 100 = 0
6.) x² + 6x = 0
III. Solve by using the quadratic formula:
7.) x² + 3x + 2 = 0
8.) 4x² – 8x = 1
9.) x² + 8x = 0
IV. Solve each equation any way you want. Show your work.
10.) x2 + 11x + 18 = 0
11.) x2 + 2x + 1 = 15
12.) 7x2 – 9x +1 = 0
13.) (x + 2)² = 36
14.) 3𝑥2−9𝑥 = −6
16.) (𝑥2 − 2𝑥 − 4)(3𝑥2 + 8𝑥 − 3) = 0.
VI. REASONING:
18.) Explain why x² = -81 DOES NOT have a solution.
15.) x² – 6x + 2 = 0
17.) (2𝑥2 −5𝑥+2)(3𝑥2 −4𝑥+1) = 0
19.) Which method can’t you use to solve this problem? x² – 47 = 0
Circle one:
Factoring
Square Roots
Quadratic Formula
Explain why:
20.) Which method can’t you use to solve this problem?
x² + 7x = 0
Circle one:
Quadratic Formula
Factoring
Square Roots
Explain why:
21.) Which method can you use to solve all quadratic equations?
Circle one:
Factoring
Square Roots
Quadratic Formula
Explain why:
22.) What are the two mistakes in setting up the quadratic formula:
Solve: 2x² – x – 6 = 0
 1  (1) 2  4(2)(6)
x
2(2)
23.) Solve this quadratic equation ALL three ways. Make sure you get the same answers!
𝑥 2 − 8𝑥 = 9
FACTORING
COMPLETING THE
SQUARE
QUADRATIC FORMULA
24.) Use any method you’d like to solve. Remember, not all quadratics can be factored!
𝑥 2 + 4𝑥 − 8 = 0
𝑥 2 + 8𝑥 + 16 = 0