Download Topic 4: Quadratic Equations a

Topic 4: Quadratic Equations
Identify a, b, and c in a quadratic equation.
Write the following in the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0, with a > 0.
1. 6x – 2𝑥 2 + 1 = 0
2. –27 = –3𝑥 2
Factor the following:
3. 5𝑥 2 − 5𝑥𝑏 − 30𝑏 2
4. 3𝑚 3 𝑛 2 – 6𝑚 4 𝑛 2
5. p + 12 – 6𝑝2
Solving factored quadratic equations. Solve:
6. (x + 3)(x – 2) = 0
7. 0 = 2p(p – 5)
8. 0 = 4(3y + 1)(y – 7)
2 2
9. m(𝑚 + ) = 0
3
Solving quadratic equations by factoring. Solve by factoring.
10. 𝑥 2 – x – 42 = 0
11. 6𝑎2 = 14a
12. −12 = 26𝑦 + 12𝑦 2
13. 2𝑥 3 + 𝑥 2 = x
14. One solution of 4𝑛 2 + 3n = 1 is:
A. 1 B. –4
C.
1
4
D. –
1
4
E. 4
(multiple choice)
ANSWERS:
1. 2𝑥 2 – 6x – 1 = 0
a = 2 b = – 6 c = –1
2. 3𝑥 2 – 27 = 0 or 3𝑥 2 +0x – 27 = 0
a = 3 b = 0 c = –27
3. 5(x + 2b)(x – 3b)
4. 3𝑚 3 𝑛 2 (1 – 2m)
5. (3 – 2p)(4 + 3p)
6. x = –3 or x = 2
7. p = 0 or p = 5
8. y = –
1
or y = 7
3
9. m = –
2
3
or m = 0
10. x = –6 or x = 7
11. a = 0 or a =
12. y = –
2
3
7
3
or y = –
3
2
13. x = – 1 or x = 0 or x =
14. C
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