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

0 votes

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

asked Jul 13, 2013 in ALGEBRA 1 by anonymous Apprentice

3 Answers

0 votes

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.

graph the equation x=y^2

answered Aug 6, 2014 by lilly Expert
0 votes

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.

graph the equation x=y^2

answered Aug 6, 2014 by lilly Expert
0 votes

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.

graph the equation x=y^2

answered Aug 6, 2014 by lilly Expert

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