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Accelerated Math 1 Study Guide
The Great Quadratic Unit
Name _____key____________________
1. Find the product: 5  8i 2  10i 
10 +50i – 16i – 80i²
10 + 34i +80
90 + 34i
2. Find the solution(s) to the given function…(to right)
The two solutions are where the graph crosses the
x-axis.
Estimated solutions: x = 1.5; x = 4.5
3. Describe the nature of the roots of the equation (what kind of solutions does it have?)
6x 2  2x  4  0
We can use the discriminant to determine the nature of the roots.
b² - 4ac = (-2)² - 4(6)(-4) = 4 – (-96) = 4 + 96 = 100
There would be two real roots to the equation since the discriminant is positive or
greater than zero.
4. Give the value of the discriminant of the equation 4 x 2  8 x  4
b² - 4ac = (-8)² - 4(4)(4) = 64 – (64) = 0
5. Find the value of c that makes the trinomial a perfect square:
x 2  40 x  c
I need to complete the square in order to find the value of c. To complete the
square I must take half the value of b and square it.
-40/2 = (-20)² = 400
x² - 40x + 400
c = 400
6. Which is the value of i 18 ?
-1
7. What is the conjugate of 6  4i ?
6 + 4i
8. Simplify:
6  7i 2
(6 – 7i)(6 – 7i) = 36 – 42i – 42i + 49i² = 36 – 84i – 49 = -13 – 84i
Complete the square. Then, name the vertex.
9. y=2x2+12x+12
½y = x² + 6x + 6
(you must get x² with a coefficient of one)
y – 6 = x² + 6x + 9
y – 6 + 9 = x² + 6x + 9
y + 3= (x + 3)²
y = (x + 3)² - 3
Vertex: (-3, -3)
10. Graph y=x2 - 2x - 15
Must put in vertex form to make it
easy to graph, or substitute values in
the function.
Vertex Form: y = (x -1)² -16
Use your graph to answer questions 11 – 15.
11. What is/are the zero(s) of the function?
-3 and 5
12. What is the interval of increase?
1 < x < infinity
13. What is the interval of decrease?
- infinity < x < 1
14. What is the line that gives the function symmetry?
X=1
15. What is the vertex of the function?
(1, -16)
Find the value of the discriminant.
16. 9x2-30x+25=0
0; one real solution
Describe the roots.
17. 3x2-4x+2=0
-8; no real solutions
Simplify.
18.
 225
19.
15i
20. ( 8 i) 3
-4
21.
-512i
22. ( 7  6 i) ( 4  3 i)
i4i 
( 8  7 i)  (1 3  2 i)
21 + 5i
23. ( 5  7 i) 2
46 + 3i
-24 – 70i
Name the conjugate.
24. 6+7i
25. -2i
6 – 7i
2i
Simplify.
26.
2  3i
2i
27.
(1 + 8i)/5
5
 6  9i
(-30 + 45i)/117
Solve each function.
28. 2 x 2  3x  4  0
X = (-3 - i√23)/4
X = (-3 + i√23)/4
29.
x 2  6 x  9  25
x = 3 + 5i
x = 3 – 5i
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