Given:
The equations of parabolas in the options.
To find:
The steepest parabola.
Solution:
We know that, if a parabola is defined as
[tex](y-k)=n(x-h)^2[/tex]
Then, the greater absolute value of n, the steeper the parabola.
It can be written as
[tex]\dfrac{1}{n}(y-k)=(x-h)^2[/tex]
[tex]p(y-k)=(x-h)^2[/tex]
where [tex]p=\dfrac{1}{n}[/tex], the smaller absolute value of p, the steeper the parabola.
Now, find the value of |p| for eac equation
For option A, [tex]|-0.5|=0.5[/tex]
For option B, [tex]|5|=5[/tex]
For option C, [tex]|8|=8[/tex]
For option D, [tex]|-10|=10[/tex]
Since, the equation is option A has smallest value of |p|, therefore, the equation [tex](x+2)^2=-0.5(y+3)[/tex] represents the steepest parabola.
Hence, the correct option is A.
