how to

Question

Sketch the graphs represented by the following equations in your answer book. Each graph must be drawn on its own system of axes : 1. Y= x^2 –x 2. Y=±√64−x^2

Answer 1

1) The equation y = x² - x

Quadratic equation represent a parabola.

Compare to parabola standard form y = ax² + bx + c.

a = 1, b = -1, c = 0

Axis of symmtry x = - b/2a

x = 1/2

Substitute x in y = x² - x.

y = (1/2)² - (1/2)

y = 1/4 - 1/2

y = - 1/4

Vertex of parabola (x,y) = (1/2, -1/4)

To find y intercept substitute x = 0 in y = x² - x

y = 0² - 0 = 0

y intercept is (0, 0)

To find x intercept substitute y = 0 in y = x² - x.

0 = x² - x

x (x - 1) = 0

x = 0 and x = 1

x intercepts are (0, 0) and (1, 0)

We need some more points for more accurate graph.

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

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

x	y = x2 - x	(x, y)
-2	y = (-2)2 - (-2) = 6	(-2,6)
-1	y = (-1)2 - (-1) = 2	(-1,2)
2	y = (2)2 - 2 = 2	(2,2)
3	y = (3)2 - 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.

Answer 2

2) The equation y = ± √64 - x²

y = ± 8 - x²

The above equation reprsents y = 8 - x² and  y = - 8 - x²

Now graph the equation y = 8 - x²

Compare to parabola standard form y = ax² + bx + c.

a = - 1, b = 0, c = 8

Axis of symmtry x = - b/2a

x = 0/-1

x = 0

Substitute x in y = 8 - x² .

y = 8 - 0²

y = 8

Vertex of parabola (x,y) = (0, 8)

To find y intercept substitute x = 0 in y = 8 - x² .

y = 8 - 0² = 8

y intercept is (0, 8)

To find x intercept substitute y = 0 in y = 8 - x².

0 = 8 - x²

x² = 8

x = ±√8

x = ± 2.82

x intercepts are (2.82, 0) and (-2.82, 0)

We need some more points for more accurate graph.

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

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

x	y = - x2 + 8	(x, y)
-4	y = -(-4)2 + 8 = -8	(-4,-8)
-1	y =- (-1)2 + 8 = 7	(-1,7)
1	y =- (1)2 + 8 = 7	(1,7)
4	y = -(4)2 + 8 = -8	(4,-8)

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...

Now graph the equation y = - 8 - x²

Compare to parabola standard form y = ax² + bx + c.

a = - 1, b = 0, c = - 8

Axis of symmetry x = - b/2a

x = 0/-1

x = 0

Substitute x in y = - 8 - x² .

y = 8 - 0²

y = - 8

Vertex of parabola (x,y) = (0, - 8)

To find y intercept substitute x = 0 in y = - 8 - x² .

y = - 8 - 0² = - 8

y intercept is (0, - 8)

To find x intercept substitute y = 0 in y = - 8 - x².

0 = - 8 - x²

x² = - 8

x = ±√8i²

x = ± 2.82 i

In this case there is no x intercepts.

We need some more points for more accurate graph.

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

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

x	y = - x2 - 8	(x, y)
-3	y =-(-3)2 - 8=-17	(-3,-17)
-2	y=- (-2)2 - 8=-12	(-2,-12)
2	y=- (2)2 - 8=-12	(2,-12)
3	y = -(3)2 - 8 = -17	(3,17)

1.Draw a coordinate plane.

2.Plot the coordinate points.

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