Question

Convert the given from of the function into the other two forms

Answer 1

Step 1: Standard form to vertex form of rows 1 and 2:

$\begin{gathered} S\tan dard\text{ form} \\ y=ax^2\text{ + bx + c} \\ \text{Vertex form } \\ y\text{ = }a(x-h)^2\text{ + k} \end{gathered}$

Standard form of row 1 to vertex form

$\begin{gathered} y=x^2\text{ - 2x - 3} \\ y=x^2-2x+1^2-3-1^2 \\ \text{y = (x -1 )}^2\text{ - 3 - 1} \\ y=(x-1)^2\text{ - }4 \end{gathered}$

Intercept form of row 3 to vertex form.

$\begin{gathered} y\text{ = (}x\text{ + 2)(x - 3)} \\ y=x^2\text{ - 3x + 2x - 6} \\ y=x^2\text{ - x - 6} \\ y=x^2\text{ - x + (}\frac{1}{2})^2\text{ - 6 - (}\frac{1}{2})^2 \\ y\text{ = (x - }\frac{1}{2})^2\text{ - 6 - }\frac{1}{4} \\ y\text{ = (x - }\frac{1}{2})^2\text{ - }\frac{25}{4} \end{gathered}$

Standard form to intercept form row 1

$\begin{gathered} y=x^2\text{ - 2x - 3} \\ \text{method: factorize} \\ y=x^2\text{ - 3x + x - 3} \\ y\text{ = x(x - 3) +1( x - 3)} \\ y\text{ = (x + 1)(x - 3)} \end{gathered}$

Intercept form to standard form row 3

$\begin{gathered} y\text{ = (x + 2)(x - 3)} \\ y\text{ = x(x - 3) + 2(x - 3) by distribution} \\ y=x^2\text{ - 3x + 2x - 6} \\ y=x^2\text{ - x - 6} \end{gathered}$

Vertice form to intercept fomr