Question

The transformations to the parent function of a quadractic equation are given below. Write an equation of the new function in vertex form.
Solve
Translated 3 units down

Answer 1

Answer:

  f(x) = x^2 -3

Step-by-step explanation:

A function is translated down 3 units by subtracting 3 from the function value. For the parent function f(x) = x^2, the translated function is ...

  f(x) = x^2 -3

_____

Comment on vertex form

The full "vertex form" has the values of the vertex coordinates in the equation explicitly. For vertex (h, k), the form is ...

  f(x) = a(x -h)^2 +k

We have moved the vertex from (0, 0) to (0, -3). The vertical scale factor (a) remains 1. So, we could write the equation as ...

  f(x) = 1(x -0)^2 -3 . . . . vertex form with unnecessary parts shown

Removing the identity elements doesn't change anything (though it requires a little practice to see them when they aren't there). So, with minor simplification, this becomes ...

  f(x) = x^2 -3