Secondary II Quadratic Practice Test
NAME__________________________ HOUR_________
Create a quadratic for each set of roots (Show work)
1.
x = 5, x = -5
2.
x = 6, x = -2
3.
x = 3 ± 4i
Graph each quadratic to find the roots; be sure to write the roots. If they are imaginary write no real roots.
4.
y = x2-3x-54
5.
f(x) = 15x2-19x-10
6.
y = x2+6x+10
Find the solutions of each quadratic by factoring (Show work)
7.
y = x2-9x+18
8.
g(x) = x2-x - 72
10.
13.
y = x2+x-6
j(x) = 2x2+10x-28
9.
b(x) = x2 +16
11.
h(x) = x2-10x+24
12.
y = x2-81
14.
x2+12x+32 = y
15.
x2-24x+140
Find the zeros of each quadratic by completing the square (Show work)
16.
m(x) = x2+2x-80
17.
y = 2x2+30x + 100
19.
y = x2-6x-4
20.
k(x) = x2+15x-5
Find the roots of each quadratic using the quadratic formula (Show work)
22.
y = x2-18x +77
23.
y = x2 - 5x - 50
25.
y = 4x2 -6x - 10
26.
y = 5x2 +7x + 11
18.
y = x2-16x+65
21.
a(x) = x2+6x+15
24.
y = x2 - 10x +14
27.
y = 6x2 -12x + 5
A snowball is thrown off the top of the auditorium and hits a teacher in the head. (Hopefully you knocked some
sense into him.) The height of the snowball as a function of seconds can be modeled by the function: g(x) =-5x2
+30x + 135 (No restrictions on solution method)
28. How high above the ground was the snowball when
it was thrown?
29. If the thrower is 5.5ft. tall, how tall is the
auditorium?
30. If the teacher moved before the snowball hit, how
many seconds would it take for the snowball to
touch the ground?
31. If the teacher is 6ft tall, when did the snowball hit
him? (Round answer to 3 decimal places)
32. How high above the thrower will the snowball
travel? How high above the auditorium?
33. How high is the snow ball at 4 seconds?
34. When will the snow ball be 160 ft. above the
ground?
35. Bonus: If the snowball travels horizontally at 50ft/s,
how far away from the auditorium was the teacher
standing?
Answers:
1.
4.
7.
10.
13.
16.
19.
y = x2 - 25
x = 9,-6
x =6,3
x = -3, x = 2
x = -7, x = 2
x = 8, -10
x =3 ± √13
22.
25.
x = 7, 11
x =5/2, -1
28.
31.
34.
135 ft
8.899 seconds
1 and 5 seconds
2.
5.
8.
11.
14.
17.
y = x2- 4x - 12
x =5/3, -2/5
x =9,-8
x = 6, x = 4
x = -4, x = -8
x =-5, -10
20.
23.
x= 2
x =10, -5
26.
29.
32.
35.
−15±7√5
−7±3𝑖√19
x = 10
129.5 ft
45 ft, 50.5 ft
444.95 ft
3.
6.
9.
12.
15.
18.
21.
y = x2- 6x +25
x = No real roots
Not factorable (x±4i)
x = -9, x = 9
x = 14, x = 10
x = 8±i
x =−3 ± 𝑖√6
24.
x = 5 ± √11
27.
30.
33.
x= 6
9 seconds
175 ft
6±√6