graph y = x^2 + x + 1

Question

the term with the appropriate definition.

Answer 1

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.

x	y = x ^2 + x + 1	(x, y )
- 1	y = (- 1)^2 + (- 1) + 1 = 1 - 1 + 1 = 1	(- 1, 1)
- 2	y = (- 2)^2 + (- 2) + 1 = 4 - 2 + 1 = 2 + 1 = 3	(- 2,3)
0	y = (0)^2 + (0) + 1 = 0 + 0 + 1 = 1	(0, 1)
1	y = (1)^2 + (1) + 1 = 1 + 1 + 1 = 3	(1, 3)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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