Question

Order the group of quadratic functions from widest to narrowest graph.

y=-9x^2, y=1/3x^2, y=-1/2x^2

Answer 1

In a quadratic function, y = a(x²) the smaller the coefficient "a", the larger is the parabola:
From widest to narrowest:

1) y=1/3x² (Widest)

2) y= -1/2x² (Wider)

3) y=-9x² (narrowest)

Answer 2

The parabola represented by equation
`y=(1)/(3)x^2` is widest

The parabola represented by equation
`y=-(1)/(2)x^2` is wider

and the parabola represented by equation
`y=-9x^2` is narrowest

Explanation:

we know that equation of parabola is given as,

`y= ax^2`

Here,

a is a constant which decide the size of parabola

if value of a is larger than the parabola will be wider

here

we have given three parabola

`y=-9x^2, y=(1)/(3)x^2, y=(-1)/(2)x^2`

and it is clear that

`-9<-(1)/(2)<(1)/(3)`

Therefore

The parabola represented by equation
`y=(1)/(3)x^2` is widest

The parabola represented by equation
`y=-(1)/(2)x^2` is wider

and the parabola represented by equation
`y=-9x^2` is narrowest