Evaluate the expression. P(8, 5) · P(7, 4) P(6, 5)

Question

Combinations and permutations

Answer 1

3 points (8,5), (7,4) and (6,5)

looks like a line of symmetry x=7

vertex has an x coordinate of x=7

( it helps to plot the points and sketch a rough graph of a parabolic

curve through the points. It's an upward opening parabola with

vertex = (7,4)

y = a(x-7)^2 + 4

plug in (8,5) or (6,5) to find a, the x^2 term's coefficient

5= a(8-7)^2 + 4

a = 5-4 = 1

y = (x-7)^2 + 4

or

y = x^2 -14x +53

check the answer, plug in the 3 points and see if they work

5=(8)^2 -14(8) +53 = 64+53 - 112 = 117-112 = 5

5 = (6)^2 -14(6) +53 = 36 -84+53 = 89-84 = 5

4 = (7)^2 -14(7) +53 = 49-98+53 = 102-98 = 4