Vertex form question

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#1

So if:

  1. b/2 takes the place of h and
  2. we’ve said that h is the x value of the vertex and
  3. b is a sort of coefficient that influences the gradient of the parabola at the y-intercept point (please correct me if that’s wrong),

that means that where the vertex is along the x axis, is directly correlated to the slope of the parabola, which would explain why our parabola shifts when we change the b value. Am I right?

But usually it also shifts on the Y axis, so I’m thinking that in the next video you’re going to tell us that c is involved in that h value too.

#2

@olidadda, I love that you’ve taken the time to consider all of these points and your reasoning is pretty good.

Unfortunately you’re not quite correct though because you’ve not considered the effects that the ‘a’ and ‘c’ terms have on the curve as well - but I really do like where you’re head is at! :slight_smile:

You’re right that the vertex will be somewhat guided by the gradient that ‘b’ is creating.
However, remember that it’s the x^2 terms that’s creating the parabola, so the ‘a’ term is also getting involved to some extend and will break your assertion that “the vertex along the x axis, is directly correlated to the slope of the parabola”.

Hopefully part 2 will fill in the blanks for you but do keep asking these sorts of questions and keep up the great work.
It’s this sort of thinking that improves your logical reasoning and problem solving skills, which in turn will make you better at maths (and programming too).

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#3

Cheers Gary!

I’ve always felt terrible at maths, maybe the fact that my Dad is a nuclear phycisist makes it hard to feel that way anyway, but now I’d like to at least restudy the stuff from high school and maybe some basic physics, I think that should serve me well, especially for VR development which is what I’m working on right now :slight_smile:

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#4

I had difficulties understanding the challenge in this section.
Switching ‘b’ into 4/2 and work out the equation.

y = (x+b/2)2 - (b/2)2 --> y = x2 + 4x

I had the impression the 'b’s would dissolve against each other plus and negative b’s

y = ((x+b/2) x (x+b/2)) - ((b/2)x(b/2)), using FOIL

But, I missed the clue to replace b for the 4, using the half.

#5

@FedPete,
Drawing it out as a square (like I do in the lecture) can help you to visualise the problem.
However, it can also help to look at the whole thing algebraically.

Assume we’re stating with x^2 + bx.
Which in squared form is (x + b/2)^2 - (b/2)^2

Let’s just look at the binomial (x + b/2)^2 for a moment.
When we expand this using FOIL we get x^2 + bx + (b/2)^2.
It’s close to what we started with but we’ve picked up an extra term at the end, which needs to be cancelled out.
So we subtract (b/2)^2 on the outside to get rid of it.

If we tried cancelling our those (b/2)^2 terms before the expansion then this would break everything and we’d only be left with x^2, meaning that we’ve lost the bx term entirely.

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#6

I have a question: If we arrive at

y = (x + 2)² - 4

wouldn’t that mean that we can shorten this to

y = x² + 4 - 4
y = x²

?

Does that make sense?

#7

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