Graphing Quadratics/Finding Local Extrema
What is the maxima of the perfect square trinomial f(x)=-3(x-2)2+4
Maxima=4
The sum of two positive numbers is 43. Find a function that models their product P, in terms of x, one of the numbers.
P=x(43-x)
A rectangular pool table is three times as long as it is wide. Find a function that models its area A in terms of its width w.
A(x) = w2/3
An Amazon ultra-delivery box has a width that is 500000 times its length and its height is 0.5 times its length. Find the function that models the volume of the box in terms of its length.
V(L) = 250,000L3
Locate the point of minima of the function x2-4x+1? Round to the nearest tenth for the values of x and y.
Minimum: (2, -3)
Find two numbers whose sum is 23 and whose product is a maximum.
11 and 12
Among all the rectangles in the whole wide world that have a perimeter of 26.5 m, find the dimensions of the rectangle with the largest area. (Do not round your answer)
6.625m x 6.625m
Based on the function:
V(x) = (x)(25)(3/x)(0.335)(2)(x)(x)(x)
Where x is equal to the length of a rectangular coffin, for what length is the volume of the coffin 10,000in3? (Round your answer to the nearest hundredth).
5.84in
State the maxima/minima, the vertex, and the x and y intercepts of the quadratic; f(x)=-x2-4x+5
Round to nearest hundredth
Vertex: (1.5, 2.75)
Minima: 1.5
x intercept:None
y intercept: (0,5)
Find two numbers whose sum is 10, such that the sum of their squares is as small as possible.
5 and 5
An isosceles boxcutter blade has a perimeter of 8.0 cm. Find the function that models its area A in terms of its base length b.
b√(4-b)
A FedEx box with a perfectly square base has a perfect volume of 240 ft3. Find the function that models its surface area.
S(x) = x2+(2880/x)
Express f(x)=4x2-24x+52 in standard form.
f(x)=4(x-3)^2+16
Two numbers add up to 24, what is the largest value of their product?
144
A pig farmer (oink oink) has 3600 ft of fencing and wants to fence off a rectangular field next to a river. However, he does not need fencing next to the river, because pigs are afraid of running water.1 What are the dimensions of the largest possible field? (Hint: find a function first).
900ft by 1800ft
An open box is to be made from a rectangular piece of cardstock, 8.5 inches wide and 11 inches tall, by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have. What size squares should be cut to create the box of maximum volume.
1.585in x 1.585in
Put the following in standard form. Find the vertex, x intercept(s) and y intercept of it and sketch the graph:
-3x2 + 6x - 2
V: (1,1)
Y intercept: ( 0, -2)
X intercepts: (.423, 0) and (1.577,0)
Standard form:
-3(x-1)2 + 1
The difference of two numbers is 14, what is the smallest possible value of their products?
-49
A test proctor with 36 feet of black curtain wants to enclose a rectangular area in a testing room and then divide it into four sections with the curtaining parallel to one side of the rectangular area.
Find the largest possible total area of the four pens. (to the nearest tenth)
32.4ft2
A design plan for a home aquarium labels it as having a rectangular base and sides while being open at the top. Its width is supposed to be x feet and its length is 2 feet more than the width. Its height is equal to the length. What is the sum of the squares of the length and width when the volume is 1000ft3?
123.5ft2