First we rewrite the table:
20 30
50 75
80 120
150 ?
We observe that for each 30 number of hops, the distance increases by 45 feet.
We must find the slope of the line:
m = (y2-y1) / (x2-x1)
m = (75-30) / (50-20)
m = 1.5
Then, the line is:
y = 1.5x
We substitute x = 150
y = 1.5 * (150)
y = 225
Answer:
Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.
100 is the easiest because 1/100 =0.01
33/100=0.33
The x coordinate of the vertex will be the average of the two zeros, here -3 and 5, so x=(-3+5)/2 = 1, f(1)=(1+3)(1-5) = -16.
Answer: (1, -16)
Let's do it some other ways. How about completing the square to turn f in to vertex form?
f(x) = (x+3)(x-5) = x² - 2x - 15 = (x² - 2x + 1) - 1 - 15 = (x-1)² - 16
and now we can read off (1, -16) as the vertex.
The other method is the vertex is x= - b/2a = - (-2)/2(1) = 1.
Three methods, same answer. Good.
Enlarging by 1.5 will make the lengths 12' and 6'. Area is L*W. 12*6=72
<span>72'^2</span>
