Question

Which equation has the steepest parabola?

Answer 1

Given:

The equations of parabolas in the options.

To find:

The steepest parabola.

Solution:

We know that, if a parabola is defined as

$(y-k)=n(x-h)^2$

Then, the greater absolute value of n, the steeper the parabola.

It can be written as

$\dfrac{1}{n}(y-k)=(x-h)^2$

$p(y-k)=(x-h)^2$

where $p=\dfrac{1}{n}$, the smaller absolute value of p, the steeper the parabola.

Now, find the value of |p| for eac equation

For option A, $|-0.5|=0.5$

For option B, $|5|=5$

For option C, $|8|=8$

For option D, $|-10|=10$

Since, the equation is option A has smallest value of |p|, therefore, the equation $(x+2)^2=-0.5(y+3)$ represents the steepest parabola.

Hence, the correct option is A.