Answer: p = 4 for (0, p) and (p, 20)
p = 20 for (4, p)
Step-by-step explanation: To find the value of p in each ordered pair, we need to plug in the given values into the function f(x) = x^2 + 4 and solve for p.
(0, p)
When x = 0, we have:
f(0) = 0^2 + 4 = 4
So the ordered pair is (0, 4), which means p = 4.
(p, 20)
When x = p, we have:
f(p) = p^2 + 4
We are also given that f(p) = 20, so we can set up the equation:
p^2 + 4 = 20
Subtracting 4 from both sides, we get:
p^2 = 16
Taking the square root of both sides, we get:
p = ±4
Since the ordered pair (p, 20) lies on the graph of f(x) = x^2 + 4, we can eliminate the negative root and conclude that p = 4.
(4, p)
When x = 4, we have:
f(4) = 4^2 + 4 = 20
So the ordered pair is (4, 20), which means p = 20.
Therefore, the values of p are:
p = 4 for (0, p) and (p, 20)
p = 20 for (4, p)