a couple algebra II questions involving parabulas?

Question

what is the equation of a aparabula?
what is the line of directrix?
how do you simplify (a/b + a) (1+1/b) -1 power
thanks in advance

Answer 1

The equation of a parabola (opening up or down) is:

y = 4p(x - h)² + k

where (h, k) is the vertex of the parabola, (h, k + p) is the focus, and y = k - p is the directrix.

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(a/b + a)(1+1/b)^(-1)
((a + ab)/b)((b + 1)/b)^(-1)
((a + ab)/b)(b/(b + 1))
(a(1 + b))/(b + 1)
a

It all simplifies to just a.

Answer 2

The meaning of "the general equation of a parabola" is not the same for everyone. Usually the first time that students see the term "the general equation of a parabola" the teacher is thinking of a parabola that opens upwards with its vertex at the origin. Thus the focus has X-coordinate 0 and Y-coordinate some positive value. If we use the notation that the focus is at (0,p), where p is positive, then the equation of the parabola is y=x^2/(4 p). Some texts later say that the "general parabola" has equation y = a x^2 + b x + c. For different choices of a, b and c, as long as a is not zero, you can get a parabola that open upwards or downwards that may or may not have its vertex at the origin. If you have a graphing calculator of computer software that will plot graphs it is fun to select values for a, b and c and plot the graph. Take values where you can factor the expression. For example y = 2x^2+5x-12 = (2x-3)(x+4). Plot it. Now change the values of 2, -3 and 4 one at a time and plot each time. Change their signs and plot.

A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

(a/b + a)(1+1/b)-1 power =
(a/b + a)(0+0) =
(a/b +a)(0) =
0

Hope this helps. :D

Answer 3

ax^2 +bx +c =0 is one equation of the parabola.

y-k = 4p(x-h)^2 is another

The directrix is a line parallel to the x-axis that is perpendicular to the axis of symmetry of the parabola. The focus and vertex bothe lie on the axis of symmetry. The directrix is the same distance from the vertex as the focus is.

(a/b+a)(1+1/b)^-1
=(a/b+a)/(1+1/b)
= [(a+ab)/b]/[(b+1)/b]
= [(a+ab)/b]/[b/(b+1)]
= (a+ab)/(b+1)
=a(b+1)/(b+1)
= a

Answer 4

so you have the parabula
ax^2 + bx + c

when the graph looks like a smiley the a of the equation is positive ( smiling is positive )

ptherwise the a is negative