# Math Help - problem into graphing form

1. ## problem into graphing form

express y+2x^2 -5x +1=0 in the form y=A(x-h)^2+k ....... so am I suppose to complete the square can someone please show the steps

2. Hello, cruxkitty!

There are a number of ways . . . Here's one of them.

Express $y+2x^2 -5x +1\:=\:0$ in the form: $y\:=\:a(x-h)^2+k$
We have: . $y +1\;=\;-2x^2 + 5x$

Divide by -2: . $-\frac{1}{2}\,y -\frac{1}{2} \;=\;x^2 - \frac{5}{2}x$

Complete the square: . $-\frac{1}{2}\,y + \frac{1}{2} + {\color{blue}\frac{25}{16}} \;=\;x^2 - \frac{5}{2}x + {\color{blue}\frac{25}{16}}$

. . and we have: . $-\frac{1}{2}\,y + \frac{17}{16} \;=\;\left(x-\frac{5}{4}\right)^2 \quad\Rightarrow\quad -\frac{1}{2}\,y \;=\;\left(x - \frac{5}{4}\right)^2 - \frac{17}{16}$

Multiply by -2: . $\boxed{y \;=\;-2\left(x - \frac{5}{4}\right)^2 + \frac{17}{8}}$