Question

Select the function that represents a parabola with vertex at (2,-1) and a point (5,8)

on its curve.
A) f(x) = (x + 2)² - 1
B) f(x) = 2(x - 2)2 - 1
C) f(x) = 2(x + 2)² - 1
D) f(x) = (x - 2)² - 1

Answer 1

Answer: D

Explanation:

A function representing a parabola takes the form of
`f(x)=a(x-h)^2+k,` where
`(h,k)` is the vertex. With a given vertex at (2,-1), then the equation is
`f(x)=a(x-2)^2-1.` This limits our choice to either choice B or choice D.

Since the parabola passes through the point (5,8), substituting this in the equation should result in a true statement.

Substituting (5,8) in choice B results in

`8=2(5-2)^2-1\\8=2(9)-1\\8=17 \text{(false)}`

Since the substitution above ended with a false statement, then choice B is incorrect.

Substituting (5,8) in choice D results in

`8=(5-2)^2-1\\8=9-1\\8=8\text{ (true)}`

Since the substitution above ended with a true statement, then choice D is the correct answer.