Question

Write three quadratic equations that are NOT equivalent, each forming a graph with vertex(-2,3).

Answer 1

Quadratic equations have the following general form:

`y=ax^2+bx+c`

The general expression for the vertex coordinates is:

`(-(b)/(2a),-(b^2)/(4a)+c)`

Then, when the vertex is (-2,3) we have:

`\begin{gathered} -(b)/(2a)=-2 \\ -(b^2)/(4a)+c=3 \end{gathered}`

From the first line, we have b = 4a

Then, for a = 1, a = 2 and a = 3, we have three diferent equations: