Question

What is the order of the quadratic functions f(x)=−0.5x2,f(x)=14x2, and f(x)=x2 from the widest graph to the narrowest graph?

Answer 1

`f(x) = - 0.5 {x}^(2) \to \: f(x) = {x}^(2) \to \: f(x) = 14 {x}^(2)`

Explanation:

The given quadratic functions are:

`f(x) = - 0.5 {x}^(2)`

`f(x) = 14 {x}^(2)`

`f(x) = {x}^(2)`

We want to order these functions, from the widest to the narrowest.

How wide the graph will open depends on the absolute value of the coefficient of the function.

The smaller the absolute value of the coefficient, the wider the graph.

Since

`| - 0.5| \: < \: |1| \: < \: |4|`

Therefore from the widest graph to the narrowest graph, we have:

`f(x) = - 0.5 {x}^(2) \to \: f(x) = {x}^(2) \to \: f(x) = 14 {x}^(2)`