The graph of a parabola is represented by the equation y=ax^2 where a is a positive integer. If a is multiplied by 2, the new parabola would become?
1. Narrower and open downward
2. Narrower and open upward
3.wider and open downward
4. Open and open upward

Question

The graph of a parabola is represented by the equation y=ax^2 where a is a positive integer. If a is multiplied by 2, the new parabola would become?
1. Narrower and open downward
2. Narrower and open upward
3.wider and open downward
4. Open and open upward

austinl · Answer

It become narrower, and opens upward.

anonymous · Answer

I think it might be answer #2. But I dont know how to explain/show my work for it.

anonymous · Answer

How though? That's what i'm mainly stuck on.

austinl · Answer

Let's work it out!

x     y=x^2    y = 2x^2
-3         9          18
-2        4           8
-1        1           2
0         0           0
1          1          2
2         4          8
3          9         18

If you graph those points, do you agree with your answer?

anonymous · Answer

How would you graph those points? ex:(-3,9) like that?

austinl · Answer

Correct.

anonymous · Answer

And yeah, i saw that same answer on a previous question exactly like mine, thats why i re asked the question.

anonymous · Answer

I thought he would have replied... (surithayer)

austinl · Answer

idk... well thanks for the medal and keep up the good work!

anonymous · Answer

$$ax ^{2}=y,x ^{2}=\frac{ 1 }{ a }y$$
it is an upward parabola ,because a is positive ,so1/a is also positive
when a is multiplied by 2,then 2a>a and1/2a <1/a so length of  latus rectum decreases
hence it becomes narrower.

anonymous · Answer

Aww wow, thanks buddy!

anonymous · Answer

yw