Question

If the parent function is y = x², explain the transformation(s) that occur to get from

the parent function to y = 3x? – 2

Answer 1

The parent function is y = x²

If we vertically stretch it by a factor of 3, then we get to y = 3x²

So it's 3 times taller than it used to be. A point like (2,4) moves to (2,12) after applying this vertical stretch. Because it's stretched vertically, it becomes more narrow in the horizontal direction.

If we then shift that down by 2 units, then we arrive at the equation y = 3x²-2

So to summarize, we applied these two transformations:

• Vertically stretch by a factor of 3
• Shift down 2 units

The graph is shown below.