Question

Determine a and k so the given points are on the graph of the function.

(1,20), (2,5); y = a (x + 1)² +k
y=(x + 1)² +
(Simplify your answers.)

Answer 1

• a = -3
• k = 32

Explanation:

You want the values of 'a' and 'k' so that the points (1, 20) and (2, 5) are on the graph of y = a(x +1)² +k.

Setup

The given (x, y) values can be used in the equation to give two equations in 'a' and 'k'.

(x, y) = (1, 20) ⇒ 20 = a(1+1)² +k = 4a +k

(x, y) = (2, 5) ⇒ 5 = a(2+1)² +k = 9a +k

Solution

Subtracting the first equation from the second gives ...

(5) -(20) = (9a +k) -(4a +k)

-15 = 5a . . . . . . simplify

-3 = a . . . . . . divide by 5

Using the first equation, we can find k:

20 = 4(-3) +k

32 = k . . . . . . . add 12

The values of 'a' and 'k' are ...

• a = -3
• k = 32