Polynomials
Characteristics of Quadratic Functions
Factoring
Square Roots
Vertex/Axis of Symmetry
100
What is the degree of the polynomial: f(x)=x7+3x5+2x-15
7
100
Describe what information the "a" value of this quadratic function gives us:
f(x) = -1/3x2+2x-3
- The graph opens concave down/ reflected over the x-axis
- The graph has an absolute maximum
- The graph is vertically compressed by 1/3
100
When we factor, we are transforming the __________ form of a quadratic function to the factored form of a quadratic function.
Standard form
100
Find the square root of 49
+/- 7
100
Find the axis of symmetry for the following equation:
f(x)= x2+2x+6
x=-1
200
What type of polynomial is this? x2+2x-5
Trinomial
200
What are the x-intercepts of this quadratic function:
f(x)=-3(x+2)(x-6)
(-2,0) and (6,0)
200
Factor the expression:
f(x)= x2-4x-12
f(x)= (x-6)(x+2)
200
Take the square root of 54
3(sqrt6)
200
Determine the second differences from the table. What type of function is this?
Second differences are all 0, linear function
300
Let J(x)=(x2+2x-3) and G(x)=(x-2). Determine the equation D(x) = J(x)+G(x)
D(x)=x2+3x-5
300
Describe the transformations shown in the equation:
f(x)= -1/4(x+5)2+2
- Reflected over the x-axis / concave down
- Shifted left 5
- Up 2
- Vertically compressed by 1/4
300
Factor the expression:
f(x)= x2+10x+16
f(x)=(x+8)(x+2)
300
Find the zeros of the expression:
(x+4)2=49
x=3, x=-11
300
Find the axis of symmetry when the x-intercepts are (-4,0) and (9,0)
x=5/2
400
Evaluate:(x+4)(x-6)
x2-2x-24
400
Determine all of the information that you can, given the equation:
f(x)=-6x2+8x+1
- Reflected over the x-axis / concave down
- Maximum
- Vertically stretched by 6
- y-intercept = (0,1)
400
Factor the expression:
g(x)= x2+5x-24
g(x)=(x-3)(x+8)
400
Find the zeros of expression:
(x+6)2=10
x= -6 +/- (sqrt10)
400
Determine the vertex of the equation:
f(x)=-6(x+5)2-4
Vertex = (-5,-4)
500
Let A(x)=x3-2x2+5, S(x)=x3+6x-5 D(x)=x2+3. Determine the function F(x)=A(x)-D(x)+S(x)
F(x)=2x3-3x2+6x-3
500
Determine all of the information that you can, given the equation:
f(x)=-2(x+2)(x+8)
- Reflected over the x-axis (Maximum)
- Vertically stretched by 2
- X-intercepts are (-2,0) and (-8,0)
500
Factor the expression:
h(x)=2x2+7x+6
h(x) = (2x+3)(x+2)
500
Find the zeros of the expression:
4(x+5)2-15=241
x=3, x=-13
500
Find the axis of symmetry. Then determine the vertex of the function:
f(x)=2x2+4x+5
Axis of symmetry: x=-1
Vertex: (-1,3)