Name________________________________
Date__________ Period__________
Algebra 2 – Test Chapter 5
1.
Write the equation of the parabola in vertex form.
a.
________________________________
b. ______________________________
6
6
5
5
4
4
3
3
2
2
1
-4
1
-3
-2
-1
1
2
3
-1
-6 -5 -4 -3 -2 -1
-2
1 2 3 4 5 6
-1
-3
Sketch a graph of the parabola with the given vertex through the given point.
2. vertex (1, 3); point (4,6)
3. vertex (-3,-2); point (1,2)
7
6
5
4
7
6
5
4
3
2
1
3
2
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
1
2 3
4 5
6 7
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
1
2 3
4 5
6 7
-4
-5
-6
-7
Graph each quadratic function. Identify the axis of symmetry and the coordinates of the vertex.
4.
y  x2  5
5.
y  x 2  4x  3
6.
y  x 2  6x  2
axis of sym: __________
axis of sym: __________
axis of sym: __________
vertex: ___________
vertex: ___________
vertex: ___________
-10 -8
-6 -4
10
10
10
8
8
8
6
6
6
4
4
4
2
2
2
-2
2
4
6
8 10
-10 -8
-6 -4
-2
2
4
6
8 10
-10 -8
-6 -4
-2
2
-2
-2
-2
-4
-4
-4
-6
-6
-6
-8
-8
-8
-10
-10
-10
4
6
8 10
4
Name________________________________
Simplify each expression.
7. (3  i )  (7  6i )
8. (3  4i )(5  2i )
Find the additive inverse of each number.
10.
 2  3i
Date__________ Period__________
11.
 7  2i
9. (4  9i )  (5  7i )
Find the absolute value of each complex number.
12.
7i
13.
 3  2i
Solve each quadratic equation by factoring, taking square roots, or quadratic formula. Find the solutions.
14. x  16  0
15. 3 x  48  0
16. x  3 x  10  0
17. 2 x  6 x  1  0
2
2
2
Factor.
18. x2 + 3x – 28
2
19. x2 – 100
Solve by completing the square. Show your work.
21. x2 + 4x – 21 = 0
20. 2x2 – 7x + 6
22. x2 – 8x – 33 = 0
Name________________________________
Date__________ Period__________
Write each function in vertex form. Sketch the graph of the function and label its vertex.
23.
y  x 2  4x  4
24.
y  x 2  4x  1
vertex form: _________________________
vertex form: ________________________
vertex: _____________
vertex: _____________
-10 -8
-6 -4
10
10
8
8
6
6
4
4
2
2
-2
2
4
6
8 10
-10 -8
-6 -4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8 10
Evaluate the discriminant of each equation.
How many real and imaginary solutions does each have?
25. x  5 x  6  0
26. 3 x  4 x  3  0
2
2
27. Find a quadratic function that includes the values in the table.
x
-2
1
5
y
-17
10
-10
28. A ball has been thrown upward from ground level. Its height h, in feet, above the ground after t seconds is
h  48t  16t 2 . Find the maximum height of the ball.
29. Suppose a parabola has a vertex in Quadrant IV and a < 0 in the equation
will the equation ax  bx  c  0 have?
2
y  ax 2  bx  c . How many real solutions
Name________________________________
Date__________ Period__________