Question

Which function is quadratic?

Function f is defined by f(x) = 1.5^x. Function g is defined by g(x) = 500x^2 + 345x

1. Function f
2. Function g

Answer 1

g(x) is a quadratic function ⇒ 2

Explanation:

• The quadratic function is the function that has 2 as the greatest power of the variable

• The form of the quadratic function is f(x) = ax² + bx + c, where a, b, and c are constant

Let us use the information above to solve the question

∵ f(x) =
`1.5^(x)`

∵ x is the exponent of the base 1.5

→ That means f(x) is not in the form of the quadratic function

∴ f(x) is not in the form of the quadratic function above

∴ f(x) does not represent a quadratic function

∴ f(x) is not a quadratic function

∵ g(x) = 500x² + 345x

∴ The greatest power of x is 2

→ That means g(x) is in the form of the quadratic function above

∵ g(x) is in the form of the quadratic function above, where a = 500,

b = 345, and c = 0 (constant values)

∴ g(x) represents a quadratic function

∴ g(x) is a quadratic function