Question

**Convert to vertex form & describe thetransformations of the following functionfrom y = x2 - 2x + 3 = 0

Answer 1

Answer:

Step-by-step explanation:

To convert the equation in standard form to vertex form, you have to use the completing square method:

$y=x^2-2x+3$

Extract a from the first two terms:

$y=a\cdot(x^2+\frac{b}{a}\cdot x)+c$

Complete the square for the expressions with x. The missing fraction is (b/(2a))². Add and subtract this term in the parabola equation

$\begin{gathered} y=a\cdot\mleft[x^2+\frac{b}{a}\cdot x+b/\mleft(2a\mright)^2-b/\mleft(2a\mright)^2\mright]+c \\ \text{Simplifying;} \\ y=a\cdot\mleft[\mleft(x+\frac{b}{2a}\mright)^2-b/\mleft(2a\mright)^2\mright]+c \end{gathered}$

Substitute the a,b and c terms respectively:

$\begin{gathered} y=a\cdot\mleft[x^2+\frac{b}{a}\cdot x+b/\mleft(2a\mright)^2-b/\mleft(2a\mright)^2\mright]+c \\ \text{Simplifying;} \\ y=a\cdot\mleft[\mleft(x+\frac{b}{2a}\mright)^2-b/\mleft(2a\mright)^2\mright]+c \end{gathered}$