Question

Which of the following graphswill display the widest parabola?Ay = –2x2 + x + 3f(x) = - x - 11

Answer 1

The widest parabola is f(x) = x²/3 - x - 11

Which of the following graphswill display the widest parabola?

A general parabola is written as:

y = ax² + bx + c

Where a is the leading coefficient. Generally, as larger is the absolute value of a, faster increasesthe function, which means that we will have a narrower parabola.

So we need to identify the leading coefficient with smaller absolute value.

For A the leading coefficient is -2, the absolute value is |-2| = 2

For B the leading coefficient is 1/3, the absolute value is |1/3| = 1/3

So B is wider.

Answer 2

The first function is,

`y=-2x^2+x+3`

The absolute value of the coefficient of x^2 in the above function is |-2|=2.

The second function is,

`f(x)=(x)/(3)^2-x-11`

The absolute value of the coefficient of x^2 in the above function is

1/3.

The graph of the parabola will be wider for the function in which the absolute value of the coefficient of x^2 is smaller.

Since the absolute value of the coefficient of x^2 is smaller in the second function than the first function, the graph of the second function will display the widest parabola.

So, the answer is

`f(x)=(x)/(3)^2-x-11`