Question

How is the graph of `y=3x^2+2` related to the graph of `f(x)=x^2`?

Answer 1

They are both quadratic functions.

Explanation:

We often write equations in the form of "functions" when there is more than one specific solution. Thus `y = ax + b`, or in this case, `y = 3x^2 + 2`, we can substitute the general symbol for a function `f(x)`, meaning that it is dependent on some 'x' values.

`y = 3x^2 + 2` is `f(x) = x^2` multiplied by 3 and offset by 2. The general shape of the plotted equation or function is the same (a parabola), but the additional terms cause the function to increase more rapidly, and to be offset from the x-axis by 2.