Alg2/Trig
Quadratics Test Review
Name _______________________
Unless otherwise indicated, show all work and check by calculator.
Questions 1 – 3: Analyze each quadratic function. Include in your analysis the following: domain,
range, vertex, y-intercept, x-intercepts*, intervals over which the function is
increasing/decreasing, end behavior, maximum/minimum points, opens up/down, and
whether the graph is wider/narrower, or the same as the parent graph ( y  x 2 ). *If the
quadratic cannot be factored, graph the function on your calculator to find the xintercepts to 2 decimal places.
1) y  3x 2  10 x  8
2) y  2( x  3)(3x  1)
Alg2/Trig
Quadratics Test Review
1
3) y  0.5( x  5)2  2
4) Given the quadratic in each row of the table, convert to the other 2 forms. Show work in the space
below the table.
Standard
Vertex
Intercept
y  5x 2  14 x  3
1
9
y  ( x  1)2 
2
2
y  (2 x  3)( x  4)
Alg2/Trig
Quadratics Test Review
2
Questions 5 – 7: Solve the quadratic graphically (calculator). Round answers to 2 decimal places.
5) x2  5x  10  6
6) 5x2  40 x  100  25
7) x2  4 x  8  5x
Questions 8 – 10: Solve the quadratic using square roots. Leave answers in simplified radical form.
8) x2  4 x  4  9
9) x2  8x  16  45
10) 9 x2  12 x  4  3
Questions 11 – 13: Solve the quadratic by completing the square. Leave answers in simplified
radical form.
11) x2  4 x  10
Alg2/Trig
Quadratics Test Review
12) x2  18x  86  0
3
13) 7 x2  28x  56  0
Questions 14 – 16: Solve the quadratic by factoring.
14) x2  15x  24  32
15) 3x2  7 x  24  13x
16) 9 x2  42 x  162  21x
Questions 17 – 20: Perform the indicated operation without a calculator and check with the
calculator.
17) (3  2i)  (4  5i)
18) (7  5i)  (6  2i)
19) (8  3i)(7  4i)
20)
(5  2i )
(3  7i)
Questions 21 – 23: Simplify the powers of i.
21) i14
22) i 39
Alg2/Trig
Quadratics Test Review
23) i 72
4
24) i123
Questions 24 – 26: Solve the quadratic by any method (not quadratic formula).
24) x2  6 x  15  0
25) 3x2  108  0
26) 20 x2  13x  21
Questions 27 – 29: Graph the quadratic without a calculator (show all supporting work), then
check by graphing on a calculator.
27) y  x 2  2 x  3
Alg2/Trig
Quadratics Test Review
28) y  ( x  1)( x  4)
5
29) y  ( x  2)2  3