Hi friends,

what does it mean when they say to draw a parabola with the following properties:

Roots =0 differs by 4 - Does this mean the x-intercepts are 0 and 4?

and lastly, f ' (-2)=0..I know to get the turning point of a parabola, one needs to use the first derivative, so does this mean to give the turning point, indicating x=-2, y=0?

if I understand the above correctly, the graph cannot be drawn..please guide me with this..I do appreciate!

juriemagic Oct 14, 2020

#1**+1 **

Have you abbreviated this Juriemagic?

It seems to have some words missing....

All I get from this is that it is a parabola with the axis of symmetry is x= -2

If the roots differ by 4... maybe it means that they are 4 units apart.

Maybe they are at (-4,0) and (0,0)

It could be concave up or concave down. The y value of the turning point cannot be determined.

So the most I can say is:

\(y=ax(x+4) \qquad \text{Where a is any real number.}\)

Melody Oct 14, 2020

#2**0 **

Hi melody,

oops, yes it is mentioned here that the range of f is \(y>=-2\)

sorry..

juriemagic
Oct 14, 2020

#3**+1 **

Well in that case it is concave up and the minimum is (-2,-2)

\(y=ax(x+4) \qquad \text{Where a is any real number.}\\ \text{passes though }(-2,-2)\\~\\ \text{Subthe point in}\\ -2=a*-2(-2+4)\\ -2=a*-4\\ a=\frac{1}{2}\\ \text{So the equation is}\\ y=0.5x(x+4)\\ y=\frac{x(x+4)}{2}\\ \)

LaTex

y=ax(x+4) \qquad \text{Where a is any real number.}\\

\text{passes though }(-2,-2)\\~\\

\text{Subthe point in}\\

-2=a*-2(-2+4)\\

-2=a*-4\\

a=\frac{1}{2}\\

\text{So the equation is}\\

y=0.5x(x+4)\\

y=\frac{x(x+4)}{2}\\

Melody
Oct 14, 2020

#4**+1 **

It's like a flower blooming...it really is not that difficult after all. In a certain sense I feel I have wasted your time on this...I should have been able to see this..anyways, as always, you are appreciated!!..Thank you..

juriemagic
Oct 14, 2020