Thank you!
2007-01-06 10:49:02 · 9 answers · asked by girl_pink 1 in Science & Mathematics ➔ Mathematics
A parabola is ONLY always the graphic image of a second powered equation such as the function:
f(x) = x^2 + x + 3
The parabola may seem visible in most even-powered functions but if you put it into a graphic calculator or actually use small numbers between let's say x = -3 and x=3, you will clearly see that the function:
f(x) = x^4
has three different "humps" to it. The number of "humps" or "hills" in a graphic equation is determined by the highest powered variable subtracted by one.
The parabola is the graphic for the function:
f(x) = x^2
because the parabola has only one "hump" and also because of the even power.
So, no, the parabola is not always the graphic of a function.
Hope this helps!
2007-01-06 11:01:49 · answer #1 · answered by Robert B 2 · 0⤊ 1⤋
No. A _vertical_ parabola is always the graph of a function, but a parabola can be twisted on its side. Consider:
x=y² (a horizontal parabola, not a function of x (although x is a function of y)
(x/â2 + y/â2) = (x/â2 - y/â2)² (a parabola tilted 45° to the right -- not a function of either x or y).
2007-01-06 11:01:29 · answer #2 · answered by Pascal 7 · 0⤊ 0⤋
Well, if you look at the standard function F(x)=x^2 the graph is obviously a function. However, the inverse of a parabola with the function f(x)=x^2 is not a function, but now it is a relation. Since for each set of x values there are 2 values for y. Thus, a parabola will be a function but a sideways one will not!
2007-01-06 10:55:10 · answer #3 · answered by Sasuke 2 · 0⤊ 0⤋
NO, parabola is ONLY the graph of a function which higher exponent is 2
y = ax^2 + bx + c (the graph of this function is a parabola always)
2007-01-06 10:52:01 · answer #4 · answered by GTA 2 · 0⤊ 0⤋
A parabola can always be described by a second-order equation in x and y. However, it is not always possible to express such a relationship as an explicit function of x. In the special case where the axis of symmetry is parallel to the y-axis, the parabola is a function of x.
2007-01-06 10:52:51 · answer #5 · answered by DavidK93 7 · 0⤊ 0⤋
Well, a function means that for any given x there will be one and only one value of y. So, try the vertical line test. Moving from left to right, is there any point on the graph where a vertical line intersects it twice? If so, then it's not a function.
2007-01-06 10:52:19 · answer #6 · answered by hunneebee22 4 · 0⤊ 0⤋
No, it is always the graph of a quadratic function (ex. y=X^2), but there are any number of kinds of functions that would have different shapes on a graph.
2007-01-06 10:51:18 · answer #7 · answered by Ape Ape Man 4 · 0⤊ 0⤋
No, because it is a quadratic graph, not a linear graph.
2007-01-06 10:52:29 · answer #8 · answered by Anonymous · 0⤊ 0⤋
I think...uh.... yay 2 points
2007-01-06 10:56:16 · answer #9 · answered by Mindes B 1 · 0⤊ 0⤋