1.Use the vertex and intercepts to sketch the graph of the quadratic function.
f(x) = -x2 - 2x + 3
A)
2.Use the Rational Zero Theorem to list all possible rational zeros for the given function.
f(x) = x5 - 3x2 + 5x + 5
C) ± 1, ± 5
3.Find the domain and range of the quadratic function whose graph is described.
The vertex is (1, 14) and the graph opens down.
B) Domain: (-∞, ∞)
Range: (-∞, 14]
4.Use the vertex and intercepts to sketch the graph of the quadratic function.
f(x) = -2(x + 5)2 - 3
B)
5.Find the range of the quadratic function.
f(x) = 2x2 - 2x - 1
D) [- , ∞)
6.Find the y-intercept of the polynomial function.
f(x) = (x - 2)2(x2 - 9)
C) -36
7.Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = (x - 1)2 - 1
A) (1, -1)
8.Graph the polynomial function.
f(x) = 4x4 + 4x3
B)
9.Find the degree of the polynomial function.
f(x) = 9x5 - 8x4 + 2
A) 5
10.Find the range of the quadratic function.
f(x) = 6 - (x + 4)2
B) (-∞, 6]
11.Find the axis of symmetry of the parabola defined by the given quadratic function.
f(x) = 6x2 - 12x - 4
D) x = 1
12.Divide using long division.
(15x3 - 5) ÷ (3x - 1)
B) 5x2 + x + -
13.Find the degree of the polynomial function.
h(x) = 10x - 5
D) 1
14.Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero.
f(x) = 5(x + 7)(x + 6)3
D) -7, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis
15.Find the axis of symmetry of the parabola defined by the given quadratic function.
f(x) = (x + 4)2 - 9
D) x = -4
16.Determine whether the function is a polynomial function.
f(x) = 5x7 - x6 + x
A) Yes
17.Graph the polynomial function.
f(x) = 3x2 - x3
D)
18.Divide using long division.
(-15x3 + 22x2 + 12x - 16) ÷ (5x - 4)
A) -3x2 + 2x + 4
19.Find the y-intercept of the polynomial function.
f(x) = 8x - x3
B) 0
20.Find the axis of symmetry of the parabola defined by the given quadratic function.
f(x) = (x + 3)2 + 9
D) x = -3
21.Use the Rational Zero Theorem to list all possible rational zeros for the given function.
f(x) = 6x4 + 4x3 - 3x2 + 2
A) ± , ± , ± , ± , ± 1, ± 2
22.Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible.
Touches the x-axis at 0 and crosses the x-axis at 4; lies below the x-axis between 0 and 4.
D) f(x) = x3 - 4x2
23.Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots.
x3 + 6x2 - x - 6 = 0
D) {1, -1, -6}
24.Divide using synthetic division.
D) x3 - 2x2 - x + 5 -
25.Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible.
Crosses the x-axis at -2, 0, and 4; lies above the x-axis between -2 and 0; lies below the x-axis between 0 and 4.
D) f(x) = x3- 2x2 - 8x
26.Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
f(x) = 3x3 + 3x2 - 5x - 5
A) falls to the left and rises to the right
27.Find the domain and range of the quadratic function whose graph is described.
The maximum is 12 at x = -1
Domain: (-∞, ∞)
Range: (-∞, 12]
28.Find the y-intercept of the polynomial function.
f(x) = -x2(x + 4)(x - 9)
A) 0
29.Find the range of the quadratic function.
f(x) = x2 + 8x - 9
A) [-25, ∞)
30.Graph the polynomial function.
f(x) = 7x - x3 - x5
B)