The equation is \"\".

\

The above equation represent the parabola.

\

To change the expression \"\" into a perfect square trinomial add and subtract (half the x coefficient)² to each side of the expression.

\

Here x coefficient = 1. so, (half the x coefficient)² = (1/2)2= 1/4.

\

Add and subtract 1/4 to the expression.

\

\"\"

\

\"\"

\

\"\".

\

Compare the equation \"\" with The standard form of the parabola with vertex (h, k ) and axis of symmetry x = h  is y = a (x - h )2 + k.

\

Vertex (h, k ) = (- 1/2, 3/4), and axis of symmetry h = - 1/2.

\

Make the table of values to find ordered pairs that satisfy the equation.

\

Choose values for x and find the corresponding values for y.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\

y

\ 		\

\"\"

\ 		\

(x, y)

\
\

 1

\ 		\

\"\"

\ 		\

 (55,1)  

\
\

-1

\ 		\

\"\"

\ 		\

(7,-1)

\
\

-2

\ 		\

\"\"

\ 		\

(1,-2)

\
\

-3

\ 		\

\"\"

\ 		\

(7,-3)

\
\

-4

\ 		\

\"\"

\ 		\

(25,-4)

\
\

1.Draw a coordinate plane.

\

2.Plot the coordinate points.

\

3.Then sketch the graph, connecting the points with a smooth curve.

\

\"graph

\

The points (55, 1), (7, - 1), (1, - 2), (7, - 3), and (25, - 4) are also on the parabola.

\

The graph is shifted right 1 unit from the origin (0, 0), and the vertex is (1, - 2). 

\