Question

The minimum of the graph of a quadratic function is located at (–1, 2). The point (2, 20) is also on the parabola. Which function represents the situation?

f(x) = (x + 1)2 + 2
f(x) = (x – 1)2 + 2
f(x) = 2(x + 1)2 + 2
f(x) = 2(x – 1)2 + 2

Answer 1

f(x) = 2(x + 1)^2 + 2

Explanation:

This question can be answered in two ways: Mathematically and Graphing.

Both are shown on the attached graph.

Mathematically:

One can solve the equations with the given values of x (-1 and 2) to see which one results in y values of (2 and 20):

Equation See the results in the attachment

f(x) = (x + 1)^2 + 2 Includes: (-1,2)

f(x) = (x – 1)^2 + 2

f(x) = 2(x + 1)^2 + 2 (-1,2) and (2,20)

f(x) = 2(x – 1)^2 + 2

Graphing

See the attached graph. Only one of the equations intersect the two given points (-1,2) and (2,20). y = 2(x+1)^2 + 2