3
QuizMultiple Choice

Mathematical Modeling: Part One — Test

Question 3 • Mathematics III

If A times x is equal to 2 x minus 4 and b times x is equal to x plus 2 , which of the following expressions produces a quadratic function?

Answer
A
open paren A plus b close paren times x
B
A b times x
C
open paren A over b close paren times x
D
open paren A minus b close paren times x

Explanation

Substitute the functions into each expression. Their product is (2x − 4)(x + 2), which expands to 2x² − 8, a quadratic because it contains an x² term. Adding or subtracting the functions gives a linear expression, and dividing them does not produce a quadratic function. So the product, choice A, produces a quadratic function.

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