Question

How to convert h(x)=(x - 2)^2 - 4 to standard form

Answer 1

To convert a function to standard form, we move all terms to the right hand side and simplify. Since all terms in this function are all on the right side already, we can begin to simplify as follows;

`\begin{gathered} (x-2)^2-4 \\ (x-2)(x-2)-4 \\ (x^2-2x-2x+4)-4 \\ x^2-4x+4-4 \\ x^2-4x \\ \text{The function now can be expressed in standard form as;} \\ h(x)=x^2-4x \\ \text{The y-intercept is derived at the point where x equals zero} \\ \text{That is, where the function crosses the y-axes} \\ \text{When x = 0, then;} \\ h(0)=0^2-4(0) \\ h(0)=0-0 \\ h(0)=0 \\ \text{Therefore the y-intercept is 0} \end{gathered}`