Quadratic functions
Find the vertex of the quadratic function y=x^2-6x +5
What is (3, -4)
Determine the degree and leading coefficient of this following: y=4x^3 -2x^2 +7x -1
Find Q(x) for P(x)= x^2 +5x + 6 divided by D(x)=x+2
What is x+3
Find the slate asymptote of f(x)= (x^2 + x + 1)/x-1
What is y=x+2
A ball is thrown upward with a velocity 32 ft/s. Its height after t seconds is given by the parabola
h(t)=32t -16t^2
What is the maximum height the ball reaches
Hint: -b/2a and h(-b/2a)
What is 16ft?
The equation y=x^2 +4x +1 in vertex form and its y intercept
What is y=(x+2)^2 -3 and (0,1)
Describe the end behavior of f(x)= -x^4 +5x^2 + 3
x--> inf, f(x)--> -inf
x--> -inf, f(x)--> -inf
(both ends down)
Use synthetic division to divide
P(x) = 2x^3 -3x^2 + 4x -5 by D(x)= x-1 and express in the form: P(x)= D(x) x Q(x) + R(x)
What is
2x^3 -3x^2 + 4x -5=(x-1) x (2x^2 -x +3) -2
Identify the vertical and horizontal asymptote of
f(x)= (2x+3)/(x-1)
A company's revenue (in $) for producing and selling x items is given by R(x)= 80x-0.5x^2
Find the maximum revenue and the number of units (x) that should be produced to obtain it
What is $3200 units and 80 units?
Find a function f(x) whose graph is a parabola that has vertex (3,−2) and passes through the point (5,6)
What is f(x)=2(x−3)^2−2
The polynomial f(x)= (x-2)^2(x+1) touches the x axis at one zero and crosses at another. Which is which?
What is it touches at x=2 and crosses at x=-1
Divide P(x)= 6x^3 +11x^2 -7x-6 by D(x)=2x +3. Find Q(x) and R(x)
What is Q(x)= 3x^2 + x -5, R(x)=9
Find the domain of the function
f(x)=(x^2 -4)/(x^2 -x-6)
(-inf, -2) U (-2,3) U (3, inf)
How long will it take the rock to reach its maximum height, and what is that height?
What is height=45m at 2 seconds?
Given y= 2x^2-8x+6, find the vertex, max or min, and y intercept
What is (2,-2), minimum, (0,6)
A polynomial with a degree of 4 has zeroes at x=-3,0,2. The zero at x=-3 has a multiplicity of 2. Write an equation for this polynomial
What is f(x)= (x+3)^2(x)(x-2)
Given f(x)= x^3 -6x^2 +11x -6 find all real zeros, then state the behavior at the x -axis and the end behavior of the graph.
What is x=1,2,3
What is crossing through the x axis
What is x—> -inf, f(x)—> -inf
x—> inf, f(x)—> inf
Determine the vertical asymptotes, holes, and horizontal asymptote of
f(x)= (x^2 -9)/(x^2 -4x +3)A football is kicked FROM THE GROUND and its height (in feet) after t seconds is given by
h(t)= -16t^2 +48t +3
How long will it take the football to hit the ground?
What is the maximum height that it reaches?
What is 3.06 seconds?
What is 39 ft?
For y= -x^2 -6x -11, find the vertex, max or min, domain, range, x intercepts, y intercept
What is Vertex=(-3,-2), maximum, Dom=all real numbers, Range=(-inf,-2], x int=DNE, y int= (0, -11)
Find the polynomial function has zeroes at x=-2, x=1, and x=3. The zero at x=-2 has multiplicity 2, and the polynomial has a leading coefficient of -2.
Write the equation for f(x) and state the end behavior.
and as x--> inf, f(x)--> -inf as x-->-inf, f(x)-->-inf
Divide D(x)= 2x^4 -3x^2 +6x +8 by P(x) x^2 -2x -3 and answer in the form of P(x)= D(x) x Q(x) + R(x)
Bonus: Is P(x) a slant asymptote of D(x), why or why not
P(x)=(x^2 -2x -3)(2x^2 + x -3) + (3x-1)
No; there is a remainder for P(x)/D(x)
Given f(x)= (2x^3 +3x^2 -x+5)/ (x^2-x-2)
Find the vertical asymptotes, horizontal asymptotes, hole, slant asymptote, and fill in the blanks:
as x—> ___, f(x)—> -inf
as x—>___, f(x)—> inf
What is vertical asymptotes at x=2,1, no horizontal asymptote or holes, slant asymptote of y=2x+5
as x—> 2 from left OR x—> -1 from left, f(x)—> -inf
as x—> 2 from right OR x—> -1 from right,f(x)->inf
At a small lavender farm, each plant produces about 67 ounces of oil per season when 400 plants are grown per acre. For each additional plant added per acre, the oil yield per plant decreases by 0.15 ounces.
The total oil yield per acre can be modeled by
A(n)= (400+n)(67-0.15n), where n=additional plants per acre. Find how many plants should be grown to maximize oil production, and what that maximum yield is.
HINT: Put it in quadratic form
What is 423 plants for 26,802 ounces per acre?