The given equation is:
p(x) = x^2 + ax - b
We write this in terms of y:
y = x^2 + ax – b
To solve for the values of the constants a and b, we are given the following conditions:
When x = 6, y = -9
When x = 1, y = 16
From these conditions, we can formulate two equation by substituting the values of y:
-9 = 6^2 + a(6) – b
6a = b – 45 ---> 1
16 = 1^2 + a(1) – b
a = b + 15 ---> 2
Combining equations 1 and 2:
6 (b + 15) = b – 45
6b + 90 = b – 45
5b = -135
b = -27
calculating for a using equation 1:
a = b + 15
a = -27 + 15
a = -12
Answers:
a = -12
b = -27