Every parabola has the base parent function of y = x2 , but when a parabola changes shape and location, here’s what’s happening to that base function:
The function y = x2 + 3 will change our parabola by moving the vertex 3 units upwards.
The function y = x2 – 4 will change our parabola by moving the vertex 4 units downwards.
The function y = (x – 1)2 will change our parabola by moving it 1 units to the right.
The function y = (x + 9)2 will change our parabola by moving it 9 units to the left.
The function y = -x2 will flip (reflect) our parabola upside down
The function y = 4x2 will make the stretch of the parabola much thinner
The function y = 1/4x2 will make the stretch of the parabola much wider
When each part takes effect, they can all wombo-combo together to give us something a lot more complicated, but still pretty straight forward. Once you understand what each part does individually, the whole is really easy to understand and plot out.