How to Transform Quadratic Equations?

If \(k>0\), the graph shifts upwards by \(k\) units:

Transformation of Quadratic Equations – Example 1:

Graph the function \(y=2x^2-5\).

Solution:

If we start with \(y=x^2\) and multiply the right side by \(2\), it stretches the graph vertically by a factor of \(2\).

Then if we subtract \(5\) from the right side of the equation, it shifts the graph down \(5\) units.

Exercises for Transformation of Quadratic Equations

Sketch the graph of each function.

• \(\color{blue}{y=-\frac{1}{2}\left(x-3\right)^2+3}\)

• \(\color{blue}{y=\left(x+2\right)^2-5}\)

• \(\color{blue}{y=-\frac{1}{2}\left(x-3\right)^2+3}\)

• \(\color{blue}{y=\left(x+2\right)^2-5}\)