How do you sketch the graph of y=x^2-5 and describe the transformation?

1 Answer
KillerBunny
May 10, 2018

See below

Explanation:

If you know the graph of a function y=f(x), then you can have four kind of transformations: the most general expression is

A f(wx+h)+v

where:

  • A multiplies the whole function, thus stretching it vertically (expansion if if |A|>1, contraction otherwise)
  • w multiplies the input variable, thus stretching it horizontally (expansion if if |w|<1, contraction otherwise)
  • h and v are, respectively, horizontal and vertical translations.

In your case, starting from f(x)=x^2, you have A=1 and w=1. Being multiplicative factors, they have non effect.

Moreover, h=0. Being ad additive factor, it has non effect.

Finally, you have v = -5. This means that, if you start from the "standard" parabola f(x)=x^2, the graph of f(x)=x^2-5 is the same, just translated 5 units down.

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