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Q: What are parabolas?
A: Parabolas are conic sections. The standard form is
The vertex is located atÂ (p,q)
â™¦ Â Note that (xp) means that the xcoordinate of the vertex is p â™¦ Â Conversely, (x+p) means that the xcoordinate of the vertex is at p
a is theÂ ‘slope’ of the parabola, determining . . . → Read More: What is a Parabola?
Q: What if I don’t have an Equation Solver, how do I graph a parabola?
A: The easiest way is to make a table of values. To keep things simple, let’s look again at . To generate a table of values, simply substitute different values of x to obtain the corresponding value of y. . . . → Read More: Graphing a Parabola
Q: What is the difference between a positive and a negative parabola?
A: The sign (+ or ) of the a value determines if the parabola opens upwards or downwards.
Let’s compare the graphs of , where a=+1 and , where a=1. . . . → Read More: Positive and Negative Parabolas
Q: What happens if I change the value of a?
A: This affects the steepness or ‘slope’ of the parabola.
Let’s compare 3 graphs with different a values: a=2, a=1, and a=0.5
Q: What happens if I change the value of p?
A: p is the xcoordinate of your vertex. If it changes, the parabola will shift left or right.
Note that the general equation for a parabola is
(xp) means:
if you have a positive p value, the result will be (xp) if you . . . → Read More: Changing the value of p in Parabola equation y=a(xp)^2+q
Q: A farmer wants to put a fence around a vegetable garden. Only three sides must be fenced, since a rock wall will form the fourth side. If he uses 40m of fencing what is the maximum area possible?
A: Â Okay, so we have two widths and one length.
The material used would . . . → Read More: A Farmer Wants to Maximize Area
Q: Two numbers hava a difference of 16. Find the numbers if their product is a minimum.
A: Let x = first number Let y = second number
Equation 1: xy = 16 Equation 2: xy=P , where P is the product.
You need to isolate for x or y in Equation 1, and . . . → Read More: Max/Min Problem, Difference of Two numbers
Formula for perimeter of a rectangle: P = 2w + 2l, where w=width and l=length
Formula for area of a rectangle: A = wl
30 = 2w+2l
40 =wl
In the area formula, isolate for l:
l = 40/w
Substitute this into the perimeter formula:
30 = 2w + 2(40/w) 30 = 2w + . . . → Read More: Math 11: A Rectangle Word Problem using the Quadratic Formula
Q: You have 128 feet of fencing to fence a rectangular area. Find the largest possible area to enclose this amount.
A: The perimeter of the space will be 128=2w+2L, where w=width and L=length
Isolate for L: L=64w
The formula for the area of the rectangle is A=w*L. Substitute L=64w into the area formula . . . → Read More: Max/Min Rectangle Problem, Maximize the Area
Q: Calculators are sold to students for 20 dollars each. Three hundred students are willing to buy them at that price. For every 5 dollar increase in price, there are 30 fewer students willing to buy the calculator. What selling price will produce the maximum revenue and what will the maximum revenue be?
A: . . . → Read More: Max/Min Problem – Maximizing Revenue, Selling Calculators


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