Answer:
Explanation:
x y
1 55
2 65
3 71
4 73
5 71
f(x) = -x^2 + 16x + 55
Steps:
Steps:
1. Calculate the average rate of change (slope) for each pair of points:
(65-55)/(2-1) = 10
(71-65)/(3-2) = 6
(73-71)/(4-3) = 2
(71-73)/(5-4) = -2
2. Use the average rate of change to calculate the y-intercept:
y-intercept = y - (slope x x)
y-intercept = 73 - (2 x 5) = 63
3. Use the y-intercept and the average rate of change to calculate the quadratic equation:
f(x) = ax2 + bx + c
f(x) = (slope x x) + bx + y-intercept
f(x) = (-2 x x) + bx + 63
4. Use the first point to calculate the value of b and c:
f(1) = (-2 x 1) + b(1) + 63
f(1) = -2 + b + 63
f(1) = 55
55 = -2 + b + 63
b = 16
5. Substitute the value of b in the quadratic equation to get the final equation:
f(x) = -x^2 + 16x + 63