Find the focus, vertex, directrix, domain, range, and graph the parabola of y= 3/2x^2

Answer 1

The function is .

The above equation represent the parabola.

The standard form of parabola equation is (x - h)^2 = 4p (y - k), where (h, k) = vertex and p = directed distance from vertex to focus.

Write the equation : in standard form of parabola.

.

Vertex : (h, k ) = (0, 0), p = directed distance from vertex to focus = 1 / 6 and Focus : (h, k + p ) = (0, 0 + (1 / 6)) = (0, 1 / 6).

Make a table; choose some values for x and find the corresponding values for y.

x		(x, y )
- 2		(- 2, 6)
- 1		(- 1, 3/2)
0		(0, 0)
1		(1, 3/2)
2		(2, 6)

Use these ordered pairs to graph the equation.

1.Draw a coordinate plane.

2.Plot the points.

3.Draw a smooth curve through these points.

Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the graph shown.

Notice that every real number is the x - coordinate of some point on the graph, so the domain is all real numbers.

But, only real numbers greater than or equal to 0 are y - coordinates of points on the graph. So the range is .

Comments

Information About Parabolas:

Form of Equation	(x - h)^2 = 4p (y - k)	(y - k)^2 = 4p (x - h)
Vertex	(h, k)	(h, k)
Axis of Symmetry	x = h	y = k
Focus	(h, k + p)	(h + p, k)
Directrix	y = k - p	x = h - p
Direction of Opening	upward if (1 / 4p) > 0, downward if (1 / 4p) < 0	right if (1 / 4p) > 0, left if (1 / 4p) < 0
Length of Latus Rectum	| 4p | units	| 4p | units

The standard form of parabola x^2 - 2x + 8y + 9 = 0 is (x - 0)^2 = 4(1/6) (y - 0).

h = 0, k = 0 and p = 1/6

Directrix is y = k - p = 0 - 1/6 = - 1/6.