Graph each equation using integer values of x from -3 to 3

Question

1. y = x squared - 2
2. y= x squared + 2
3. y= -x squared + 3

Answer 1

1).

The equation is y = x² - 2.

The standard form of parabola equation is y = ax² + bx + c.

So, the given equation represents a parabola.

The vertex form of parabola equation is y = a(x - h)^2 + k, where (h, k) = vertex and axis of symmetry x = h.

The parabola is y = x² - 2.

Write the equation in vertex form of a parabola eqaution.

y = 1(x - 0)² - 2.

Compare the equation with the vertex form of the parabola equation.

Vertex (h, k) = (0, - 2), and axis of symmetry x = 0.

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 - 0)2 - 2	(x, y)
- 3	y = (- 3 - 0)2 - 2 = (- 3)2 - 2 = 9 - 2 = 7	(- 3, 7)
- 2	y = (- 2 - 0)2 - 2 = (- 2)2 - 2 = 4 - 2 = 2	(- 2, 2)
- 1	y = (- 1 - 0)2 - 2 = (- 1)2 - 2 = 1 - 2 = - 1	(- 1, - 1)
0	y = (0 - 0)2 - 2 = 0 - 2 = - 2	(0, - 2)
1	y = (1 - 0)2 - 2 = (1)2 - 2 = 1 - 2 = - 1	(1, - 1)
2	y = (2 - 0)2 - 2 = (2)2 - 2 = 4 - 2 = 2	(2, 2)
3	y = (3 - 0)2 - 2 = (3)2 - 2 = 9 - 2 = 7	(3, 7)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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

Answer 2

Contd........

2).

The equation is y = x² + 2.

The vertex form of parabola equation is y = a(x - h)^2 + k, where (h, k) = vertex and axis of symmetry x = h.

The parabola is y = x² + 2.

Write the equation in vertex form of a parabola eqaution.

y = 1(x - 0)² + 2.

Compare the equation with the vertex form of the parabola equation.

Vertex (h, k) = (0, 2), and axis of symmetry x = 0.

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 - 0)2 + 2	(x, y)
- 3	y = (- 3 - 0)2 + 2 = (- 3)2 + 2 = 9 + 2 = 11	(- 3, 11)
- 2	y = (- 2 - 0)2 + 2 = (- 2)2 + 2 = 4 + 2 = 6	(- 2, 6)
- 1	y = (- 1 - 0)2 + 2 = (- 1)2 + 2 = 1 + 2 = 3	(- 1, 3)
0	y = (0 - 0)2 + 2 = 0 + 2 = 2	(0, 2)
1	y = (1 - 0)2 + 2 = (1)2 + 2 = 1 + 2 = 3	(1, 3)
2	y = (2 - 0)2 + 2 = (2)2 + 2 = 4 + 2 = 6	(2, 6)
3	y = (3 - 0)2 + 2 = (3)2 + 2 = 9 + 2 = 11	(3, 11)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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

Answer 3

Contd........

3).

The equation is y = - x² + 3.

The vertex form of parabola equation is y = a(x - h)^2 + k, where (h, k) = vertex and axis of symmetry x = h.

The parabola is y = - x² + 3.

Write the equation in vertex form of a parabola eqaution.

y = - 1(x - 0)² + 3.

Compare the equation with the vertex form of the parabola equation.

Vertex (h, k) = (0, 3), and axis of symmetry x = 0.

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 - 0)2 + 3	(x, y)
- 3	y = - (- 3 - 0)2 + 3 = - (- 3)2 + 3 = - 9 + 3 = - 6	(- 3, - 6)
- 2	y = - (- 2 - 0)2 + 3 = - (- 2)2 + 3 = - 4 + 3 = - 1	(- 2, - 1)
- 1	y = - (- 1 - 0)2 + 3 = - (- 1)2 + 3 = - 1 + 3 = 2	(- 1, 2)
0	y = - (0 - 0)2 + 3 = 0 + 3 = 3	(0, 3)
1	y = - (1 - 0)2 + 3 = - (1)2 + 3 = - 1 + 3 = 2	(1, 2)
2	y = - (2 - 0)2 + 3 = - (2)2 + 3 = - 4 + 3 = - 1	(2, - 1)
3	y = - (3 - 0)2 + 3 = - (3)2 + 3 = - 9 + 3 = - 6	(3, - 6)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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