2.1
(5-2i)+(3+3i)
5-2i+3+3i
(5+3)+(-2+3)I
8+I
Name the Vertex, x-intercepts and y-intercepts of
f(x)=(x-1)^2-2
vertex: (1, –2)
x-intercepts:
0=(x-1)^2-2
x=-1 plus or minus sqr. root 2
x=1 plus or minus sqr. root 2
y-intercept:
f(0)=-1
which best describes the graph of the function f(x)= x3+3x2-4x-12?
It goes down to the far left and up to the far right.
Divde
x^4+2x^3-4x^2-5x-6 divided by x^2+x-2
x^2+x-3-12/x^2+x-12
divide
x^4-256 divided by x-4
x^3+4x^2+16x+64
(5+4i)(6-7i)
58-11i
f(x)=2(x+2)^2-1
Name the Vertex, x & y-intercetps and domain and range
vertex (-2,-1)
x-intercepts: -2 plus or minus sqr. root 2/2
y-intercept: f(0)=7
domain (-inf,+inf)
range [-1,+inf)
Find all of the zeros of the function:
f(x) = 9x3 - 24x2 + 16x
To find all of the zeros of the function:
f(x) = 9x3 - 24x2 + 16x
factor:
f(x) = x(9x2 - 24x + 16)
f(x) = x(3x - 4)(3x - 4)
To find the zeros, where the graph crosses the x-axis, set y = f(x) to zero, and solve for "x":
0 = x(3x - 4)(3x - 4)
Using the zero product property:
x = 0 or x = 4/3
The correct answer is: x = 0, 4/3
Divide
x^7+x^5-10x^3+12 divided by X+2
x^6-2x^5+5x^4-10x^3+10x^2-20x+40-68/x+2
Graph the equation. Must include vertex, and at least one point on each side. -x^2 -6x + 1 = 0
Graph on the board
5+4i/4-i
16/17+21/17i
Tell if the parabola opens up or down, has a max or min, state the max or min and give the domain
f(x)=-2x^2-12x+3
a = –2. The parabola opens downward and has a maximum value.
b. The maximum is 21 at x = −3 .
domain: ( ,) −∞ ∞ range: (−∞, 21]
f(x)=3x^2-x^3
(a)Give the graphs end behavior
(b) Find x-intercepts and state if the graph crosses or touches the axis
(c) Find the y-intercept
a)rises to the left and falls to the right
b) -x^3+3x^2=0
-x^2(x-3)=0
x = 0, x = 3 The zero at 3 has odd multiplicity so f(x) crosses the x-axis at that point. The root at 0 has even multiplicity so f(x) touches the axis at (0, 0).
c) f(0)=-(0)^3+3(0)^2=0
The y-intercept is 0.
divide
2x^5-8x^4+2x^3+x^2 divided by 2x^3+1
x^2-4x+1+4x-1/2x^3+1
Name the vertex 2x^2 + 4x - 6 = 0?
vertex (-1,-8)
x^2-6x+10=0
x=3+i and 3-i
Tell if the parabola opens up or down, has a max or min, state the max or min and give the domain
f(x)=6x^2-6x
a = 6. The parabola opens upward and has minimum value.
b. The minimum is 3 2 − at x=1/2
c. domain: (−∞ ∞)
range: [3/2,∞)
Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers f(-1) & f(0)
f(x)=2x^4-4x^2+1
f(–1) = –1 f(0) = 1 The sign change shows there is a zero between the given values.
Use synthetic division and the Remainder Theorem to find the indicated function value
f(x)=2x^3-11x^2+7x-5; f(4)
f(4)=-25
Among all pairs of numbers whose sum is 20, find a pair whose product is as large as possible. What is the maximum product?
10 and 10:100
4x^2+8x+13=0
{-1+3/2i, -1-3/2i}
A ball is thrown upward and outward from a height of 6 feet. The height of the ball f(x), in feet, can be modeled by f(x)=-0.8x^2+2.4x+6 where x is the ball's horizontal distance, in feet, from where it was thrown.
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
b. How far does the ball travel horz. before hitting the ground?
The vertex is (1.5, 7.8). The maximum height of the ball is 7.8 feet. This occurs 1.5 feet from its release.
The ball will hit the ground when the height reaches 0.The ball travels 4.6 feet before hitting the ground.
Find the zero for the polynomial and give the multiplicity for each zero
f(x)=4(x-3)(x+6)^3
f(x)= 4(x-3)(x+6)^3
x = 3 has multiplicity 1; The graph crosses the x-axis. x = –6 has multiplicity 3; The graph crosses the x-axis.
Use synthetic division to divide
f(x)=x^3-2x^2-x+2 by x+1 and use the result to find all zeros of f
x^2-3x+2; -1, 2, 3
Find the zero for the polynomial and give the multiplicity for each zero
f(x)=2(x-5)(x+4)^2
f(x)=2(x-5)(x+4)^2
x = 5 has multiplicity 1; The graph crosses the x-axis. x = –4 has multiplicity 2; The graph touches the x-axis and turns around.