Download Quadratics Study Guide Solve the equation using the Zero

Quadratics Study Guide
Solve the equation using the Zero-Product Property.
1.
a.
b.
c.
d.
1 6
 , 
5 7
1 6
 ,
5 7
0, 6
7
0,  6
7
a.
b.
c.
d.
4, 3
–1,1
4,3
–4, 3
a.
b.
c.
d.
2, 1
–3, 9
–2, 1
2, 1
c.
d.
–2, 2
no real number solutions
a.
b.
c.
d.
–7, 7
–49, 49
b.
c.
d.
0, –10
a.
b.
c.
d.
–7, 7
–7, –7
7, 7
7, –7
3.
2.
Solve the equation using square roots.
4.
a. –3, 3
b. –9, 9
c.
d. no real number solutions
6.
5.
a.
b. –4, 4
What are the solutions of the equation?
7.
a.
b.
no real number solutions
0,
0, 10
11.
c.
d.
Simplify the product using the distributive property.
8.
a.
b.
9.
12.
c.
a.
b.
d.
c.
d.
a. 1, –5
b. 1, 5
c. –3, 5
d. –3, –5
10.
a.
13.
a.
b.
c.
d.
1, –
Simplify the radical expression.
14.
a.
10
b.
c.
d.
d.
10 5
16. The area of a rectangular painting is given by the
trinomial x2 + 4x – 60. What are the possible dimensions
of the painting? Use factoring.
a. x – 6 and x + 10
b. x + 6 and x – 10
c. x – 6 and x – 10
d. x + 6 and x + 10
10 10
15.
a.
b.
16
8 2
c. 10
Simplify the product using FOIL.
17. (3x – 7)(3x – 5)
a.
a. 9x2 + 6x + 35
b.
b. 9x2 + 36x + 35
c.
c. 9x2 – 36x – 35
2
d.
d. 9x – 36x + 35
18.
Solve the equation by completing the square. Round to the nearest hundredth if necessary.
d. 1.52, –8.52
19.
21. The area of a rectangular barnyard is given by the
a. –5, 3
trinomial 6x 2 + 11x – 35. What are the possible
b. –5, –3
dimensions of the barnyard? Use factoring.
c. 5, 3
a. 3x – 5 and 2x + 7
d. 5, –3
b. – 3x – 5 and –2x – 7
20.
c. 3x – 3 and 2x + 7
a. 1.52, 8.52
d. 3x + 5 and 2x – 7
b. –1.52, –8.52
c. –1.52, 8.52
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
22.
24.
a.
b.
c.
d.
–3.56, 0.56
–3.56, –0.56
3.56, –0.56
3.56, 0.56
a.
b.
c.
d.
–5, –2
5, –2
–5, 2
5, 2
a.
b.
c.
d.
23.
25.
a.
b.
c.
d.
What is the factored form of the expression?
Simplify the radical expression by rationalizing the denominator.
a.
b.
c.
d.
26.
a.
b.
c.
d.
27. What is the value of c such that
perfect-square trinomial?
is a
7
98
196
49
28. What is the value of c such that
perfect-square trinomial?
a.
11

2
b. 121
c. 121
2
is a
d.
121
4
29. The area of a rectangular garden is given by the
trinomial x2 + 4x – 45. What are the possible dimensions
of the rectangle? Use factoring.
Simplify the product.
30. 5a2(3a4 + 3b + 2)
a. 8a4 + 8ab + 5a2
b. 15a8 + 3b+ 10a2
c. 15a6 + 15a2b + 10a2
d. 8a6 + 15a2b + 5a2
31. 8p(–3p2 + 6p – 2)
a. –5p3 + 14p2 – 6p
b. 48p2 – 16p – 24p3
Factor the polynomial.
33.
a. 2x(x2 + 2x + 4)
b. 2x(x + 2)(x + 4)
c. 2x(x2 + 2x + 8)
d. 2x3 + 4x2 + 8x
34. 25w6 + 35w3
a. 5w2 (5w4 + 7w)
b. 5w3 (5w3 + 7)
c. w3(25w3 + 35)
d. 5(5w6 + 7w3)
35. The area of a rectangular pool is given by the trinomial
9y2 + 12y – 45. What are the possible dimensions of the
pool? Use factoring.
a. 3y + 5 and 3y – 9
b. 3y – 3 and 3y + 9
c. 3y – 5 and 3y + 9
d. – 3y – 5 and –3y – 9
What method(s) would you choose to solve the
equation? Explain your reasoning.
36.
a.
Quadratic formula, graphing; the equation cannot be
factored easily since the numbers are large.
b. Square roots; there is no x-term.
c. Quadratic formula, completing the square or
graphing; the coefficient of x2 -term is 1, but the
equation cannot be factored.
d. Factoring; the equation is easily factored.
37.
a. Square roots; there is no x-term.
b. Quadratic formula, graphing; the equation cannot be
factored easily since the numbers are large.
c. Factoring; the equation is easily factored.
d. Quadratic formula, completing the square or
graphing; the coefficient of x2 -term is 1, but the
equation cannot be factored.
a.
b.
c.
d.
x + 9 and x – 5
x – 9 and x – 5
x + 9 and x + 5
x – 9 and x + 5
c. 14p2 – 6p – 5p3
d. –24p3 + 48p2 – 16p
32. 2n(n2 + 3n + 4)
a. 2n3 + 6n2 + 8n
b. 2n3 + 3n + 4
c. 2n3 + 6n + 8
d. n2 + 5n + 4
Quadratics Study Guide
Answer Section
MULTIPLE CHOICE
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D
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B
D