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# Intro to parabola transformations

Sal discusses how we can shift and scale the graph of a parabola to obtain any other parabola, and how this affects the equation of the parabola. Created by Sal Khan.

## Want to join the conversation?

• How does :y-k=x^2 shift the paraobla upwards?
• y - k = x^2 is the same as
y = k + x^2

so if k = 5 and x = 0 you get

y - 5 = 0, which is y = 5, shifting the parabola up by 5
• Why when we are subtracting k from y the parabola is shifting upwards instead of downwards?
• The reason the graph shifts up instead of down when you subtract a number from y is because (if you think about it) subtracting from y is the same as adding that number to the opposite side of the equation which results in a higher end value for y.
Does that help?
• Why is there not explanation to k being a negative when its climbing up.

I'm glad I've read information on these before hand otherwise I'd be very confused. The form for shifting I've seen at least for up down left right is:
y = (x-h) + k
H goes left and right
K goes up and down
Say we have the equation:
Y-k=x^2
To see how this shifts the parapola up k units, substitute x with 0. The equation will simplify to y-k=0.
So for the equation to be true y needs to be equal to k; like how in factored form x needs to be the inverse of the constants a or b to equal 0, i.e (x-a)(x+b)=0
• The ending gragh with parabolas looks like a spider!!
• I want to give a concrete example to anyone that might want one:

Let's take the example of apples. Instead of a parabola, I'm going to do a linear function, y = x.

Let's name y 'Yalena' and x as 'Xavier'.

When Yalena has 1 apple, Xavier has 1 apple.
When Yalena has 2 apples, Xavier has 2 apples.
When Yalena has 3 apples, Xavier has 3 apples.

Alright. Now, let's make it so Yalena always has 1 more apple than Xavier. We'll make the equation y = x + 1.

When Xavier has 1 apples, Yalena has 2 apples.
When Xaiver has 2 apples, Yalena has 3 apples.
When Xavier has 3 apples, Yalena has 4 apples.

Now, we can use this type of thinking to understand y - k = x. Let's do y - 1 = x. Or, in other words, Xavier has 1 less apple than Yalena!

When Yalena has 1 apple, Xavier has 0 apples.
When Yalena has 2 apples, Xavier has 1 apples.
When Yalena has 3 apples, Xavier has 2 apples.

We can do this in the other direction, too. If we know that Xavier has 1 less apple than Yalena, we know that Yalena has 1 more apple than Xavier. So, if we know how many apples Xavier has, we'll know how many Yalena has.

Again: y - 1 = x
Xavier has 1 apple. That's one less than Yalena has, so she must have 2.
Xavier has 2 apples. That's one less than Yalena has, so she must have 3.

And so on and so on and so on.

I hope this helps someone :)
• What age group is this for as I am in 5th grade and would like to know what to study and if I am studying something to high level or to low level for me.
• This is a concept that is studied in Algebra II, a class taken in 10th or 11th grade. This will probably be above your level, because it relies on concepts that aren't taught until Algebra I or Algebra II.
As for topics to study currently, if you are seeking help for what you're currently learning, simply search for that. If you want to get ahead, then it might be a good idea to start watching some of the videos under Algebra Basics. It's a good foundation in the concepts that will be introduced in middle and high school.
• Isn't vertex form y=(x-h)^2+k? Why is he saying y-k=(x-h)^2?
• if you subtract the "k" from the right side you get Sal's equation.
• When he writes "y - k = x^2" and says that the yellow curve is basically shifted up so it's like the blue curve, wouldn't it be simpler to say that "y - k = x^2" is the same thing as "y = x^2 + k" and that's why the blue curve is higher because we're adding to the "x^2"?
• Yes, correct. I prefer the form you suggested instead of y - k = x^2. It's more intuitive.