Section 1.4A - Quadratic Equations
Name___________________________________
Zero Product Property, Square Root Property, Complete the Square, Solve by Complete the Square
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
Provide the missing information.
equation is a second degree equation of the form ax2 + bx + c = 0 where a
1) A
2) A
equation is a first degree equation of the form ax + b = 0 where a
3) The zero product property indicates that if ab = 0, then
= 0 or
4) The zero product property indicates that if (5x + 1)(x - 4) = 0, then
5) The square root property indicates that if x2 = k, then x =
0.
= 0.
= 0 or
8) t2 - 9t = -14
9) y2 - 15y = 0
10) 10m(m + 3) = 13m - 3
11) 16s2 = 25
Solve the equation by using the square root property.
15
12
=12) t 4
16
13) p2 = 81
14) (7x + 4)2 = 81
1
= 0.
.
6) The value of n that would make the trinomial x2 + 20x + n a perfect square trinomial is
Solve the equation.
7) 5w (5w + 16) = -64
0.
.
15) (c - 5)2 = 16
16) (3z - 18)2 + 58 = 40
Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial.
17) j2 - 18j + n
18) x2 + 20x + n
19) Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial.
14
t2 t+n
3
Solve the quadratic equation by completing the square and applying the square root property.
20) u2 + 8u + 17 = 0
21) n2 + 12n = -17
22) y2 + 34 = 10y
23) 2v2 + 8v + 22 = 0
24) 2x2 + 6 = 9x
25) -5v2 = 4 + 7v
2
Answer Key
Testname: SECTION 1.4A QUADRATIC EQUATIONS
1) quadratic
2) linear
3) a; b
4) (5x + 1); (x - 4)
5) ± k
6) 100
8 8
7) - , 5 5
8) {7, 2}
9) {0, 15}
1 3
10) - , 5 2
11) 12)
5 5
,
4 4
15
1
±
i
4
4
13) {±9}
5 13
14) , 7
7
15) {9, 1}
16) {6 + i 2, 6 - i 2}
17) n = 81; (j - 9)2
18) n = 100; (x + 10)2
19) n =
49
72
; t9
3
20) {-4 ± i}
21) {-6 - 19, -6 + 19}
22) {5 - 3i, 5 + 3i}
23) {-2 - i 7, -2 + i 7}
24)
9 - 33 9 + 33
,
4
4
25) -
31
31
7
7
i, +
i
10 10
10
10
3