Order the group of quadratic functions from widest to narrowest graph.
y=-4x^2 y=-3x^2 y= -5x^2

Question

Order the group of quadratic functions from widest to narrowest graph. 
y=-4x^2 y=-3x^2 y= -5x^2

debbieg · Answer

$\Large y=ax^2$ is a vertical stretch of $\Large y=x^2$ by a factor of |a|.

The larger the |a| is, the more "severe" the stretch, and thus, the thinner the parabola will be.

debbieg · Answer

Eg, compare these: https://www.desmos.com/calculator/fil92slsav

anonymous · Answer

this stuff confuses me, I hate Algebra

debbieg · Answer

Using those as comparison/example, can you figure out your problem?

anonymous · Answer

ugh no "(

debbieg · Answer

OK, did you read what I wrote above? If you don't understand something, ask questions.

anonymous · Answer

I don't understand it at all

debbieg · Answer

If you just keep saying "I hate algebra" and "I'm confused", you will continue to be confused, and probably continue to hate algebra. 

You have to work to understand it.

debbieg · Answer

Do you know what the graph of $y=x^2$ looks like? The shape of the basic graph?

anonymous · Answer

I am working on it.. it's just hard for me to grasp.

anonymous · Answer

yes i know what it looks like

debbieg · Answer

OK, do you understand what happens when you multiply that function by 2? E.g.....

$\Large y=2x^2$

What does that factor of 2 "do" to the shape of the graph?

anonymous · Answer

makes it thinner

debbieg · Answer

THINK about exactly HOW it's acting on the function, as compared to the original:

For every value of x, you still start by computing $\Large x^2$, right?

THEN you take THAT and multiply by 2, to get your y: $\Large y=2x^2$


So in the original function, $\Large y=x^2$, if you have x=2 you get y=4.
In the new function, $\Large y=2x^2$, if you have x=2, you get y=2*4=8
.
So in the original function, $\Large y=x^2$, if you have x=3 you get y=9.
In the new function, $\Large y=2x^2$, if you have x=3, you get y=2*9=18.

debbieg · Answer

RIGHT! because it "stretches" it vertically (up). It's like, if you could grab the graph where it extends in the parabola, and literally "pull" it upward.

debbieg · Answer

Now, instead of multiplying by 2, suppose I multiply by... 5. So I have:  $\Large y=5x^2$


So in the original function, $\Large y=x^2$, if you have x=2 you get y=4.
In the new function, $\Large y=5x^2$, if you have x=2, you get y=5*4=20

So in the original function, $\Large y=x^2$, if you have x=3 you get y=9.
In the new function, $\Large y=5x^2$, if you have x=3, you get y=5*9=45.

debbieg · Answer

So again, it's thinner than the original... and also thinner than the first modification, $\Large y=2x^2$ because it is a more dramatic stretch.

Like I said above: The larger the |a| is, the more "severe" the stretch, and thus, the thinner the parabola will be.

Now for your functions, a is negative, but that doesn't have anything to do with the stretch or how thin/wide the resulting parabola is. That simply means that it flips the parabola over.

So again, all that matters for the thinness/width of the parabola, is the ABSOLUTE VALUE of x - how big the number is, not whether it is positive or negative.

So ignore the negative sign, and just look at the |a| (the coefficient of x). The bigger it is, the "more severe" the stretch, and hence, the THINNER the parabola.

anonymous · Answer

Okay I understand that now , I just gotta learn how to get the answer in y= such and such form

anonymous · Answer

oh nvm i see now !

anonymous · Answer

duh that was so easy once i looked at the graph

debbieg · Answer

:)