Question

The transformations to the parent function of a quadratic equation are given below.Write an equation of the new function in vertex form. Note: ^ denotes "raised to thepower of"Transformations: translated 3 units downA y = -x^2 +3B y = -x^2 - 3C y = x^2 + 3D y = x^2-3

Answer 1

Vertical translations

Suppose k> 0

y = f (x) + k, shift the graph up k units.

y = f (x) -k, shift the graph k units down.

so:

`\begin{gathered} Let\colon \\ f(x)=x^2 \\ \end{gathered}`

translated 3 units down:

`\begin{gathered} y=f(x)-k \\ k=3 \\ so\colon \\ y=x^2-3 \end{gathered}`