Name
Chapter 7 – Quadratics Review
To ensure an opportunity for partial credit, please show all work for every question.
1.
Write a quadratic equation, with integral coefficients, which has roots of 2/3 and 1/6.
(7 points)
2.
Graph the inequality y > x2 + 4x – 3. Is the point (2, 3) in the solution set? Justify your
answer. Is the point (-1, -6) in the solution set? Justify your answer.
(10 points)
3. Given the following table, state all integer values which represent a real root. State all pairs
of consecutive x-values between which a real root lies.
(4 points)
x
-7
-6
-5
-4
-3
-2
-1
0
1
y
0
-3
-7
-1
2
5
0
-2
4
4. Solve the system of equations algebraically.
x2 + y2 = 29
y–x=3
(10 points)
5. A small group of college football players are tossing a football around. One student holds
the ball in front of him then releases the ball and kicks the football in the air. The height of
the football can be found using the equation h(x) = -16x2 + 56x + 2, where h(x) represents
the height of the ball and x is the time since the ball was kicked. When will the football
reach its maximum height? What is the maximum height of the ball? When will the football
be 42 feet in the air? (Only an algebraic solution will receive full credit)
(8 points)
6.
State the sum and the product of the roots of the equation 0 = -x2 + 3x – 8
(2 points)
7.
Write a quadratic equation that has imaginary roots.
(4 points)
8.
Find the value of a such that the roots of the quadratic equation 0 = ax2 – 6x + 4 are equal.
(4 points)
9.
Find all values of c such that the roots of the equation 2x2 + 8x + c = 0 are imaginary.
(4 points)
10. State the axis of symmetry and the vertex of the parabola given by the equation
y = 3x2 - 12x + 8
(2 points)
11. Write a quadratic equation that has a root of 9 – 2i.
(5 points)
12. Given the graph below: How many unique real roots does the function have? State an
integer value that represents a real root. State BOTH pairs of consecutive x- values between
which a real root lies?
(4 points)
13. Using the graphing calculator, approximate all real roots, to the nearest hundredth, of the
function 0 = -2x3 – 5x2 + 3x + 6.
(3 points)
14. If 2x2 + kx – 9 = 0 and one root of the equation is ½, find the other root and the value of k.
(6 points)
15. If the sum of the roots of a quadratic equation is 6 and the product of the roots is 10, write
the quadratic equation and then find the roots, in simplest form.
(8 points)
16. Solve the system of equations either algebraically or graphically.
y = -x2 + 4x + 1
y = 3x + 5
(7 points)
17. Describe the number and nature of the roots of the equation 5x2 – 4x – 1 = 0. How many xintercepts will the graph of the equation have?
(5 points)
18. The value of the discriminant for the graph shown would be ____________ (positive,
negative or zero)
(1 point)
19. If one root of 2x2 + 8x + k = 0 is 5, find the other root and the value of k.
(6 points)