Question

PLEASE HELP ME ASAP?!?

(look at the image)
What is the order, from widest to narrowest graph, of the
quadratic functions f(x) = -0.5x2, f(x) = 1/4x2, and f(x) = x2?

Answer 1

f(x) =
`(1)/(4)x^(2)` > f(x) = -0.5x² > f(x) = x²

Explanation:

In a quadratic function leading coefficient decides the width of a graph.

In simpler words, leading coefficient decides the vertical stretch of the graph.

Higher the value of leading coefficient, higher the vertical stretch.

When a graph is vertically stretched it becomes narrower.

(Note: Minus sign of the coefficient decides the opening of the graph, upwards or downwards)

Therefore, f(x) = x² having coefficient = 1 is the narrowest and f(x) =
`(1)/(4)x^(2)` will be the widest.

So the descending order will be,

f(x) =
`(1)/(4)x^(2)` > f(x) = -0.5x² > f(x) = x²