Question

write each function in vertex form:
1) y=x^2-4x+6
2) y=4x^2+7x
3) y=-2x^2+8x+3

Answer 1

\(\large \begin{align} \color{black}{\text{vertex form of parabola:}~~y=(a-h)^2+k\\~\\~\\
y=x^2-4x+6\\~\\~\\
\color{blue}{\text{this is little similar to squaring method of quadratic function}}\\~\\~\\

=(x^2-4x+4)-4+6\\~\\~\\
=(x-2)^2+2\\~\\~\\

\text{vertex(h,k)=(2,2)}
}\end{align}\)

Answer 2

*quadratic equation

Answer 3

second equation is of the form

(ax+b)^2=(ax)2+2axb+b^2

try to make adjustment to make it perfect square

Answer 4

*(ax+b)^2=(ax)^2+2axb+b^2