Finding the y Intercepts of a Horizontal Parabola

[Jason76]

What would be the first step? I know that to find the x intercepts of a vertical parabola, you must factor it, or use the quadratic formula.

 

[Deleted member 4993]

What would be the first step? I know that to find the x intercepts of a vertical parabola, you must factor it, or use the quadratic formula.

What is the definition of y-intercept ?

 

[DrPhil]

What would be the first step? I know that to find the x intercepts of a vertical parabola, you must factor it, or use the quadratic formula.

"x" and "y" are completely arbitrary names. You could just as well call them "p" and "q". There is no reason you can't have x be a function of y. Since by definition a "function" is single-valued, a horizontal parabola can only be expressed by x as a function of y. Just do it.

 

[Jason76]

What is the definition of y-intercept ?

A y intercept is where the parabola crosses the y axis.

 

[Deleted member 4993]

A y intercept is where the parabola crosses the y axis.

So what is the value of 'x' on y-axis?

Now substitute that value into your function and evaluate 'y'(/s). You evaluated your y-intercept/s.

 

[Jason76]

So what is the value of 'x' on y-axis?

Now substitute that value into your function and evaluate 'y'(/s). You evaluated your y-intercept/s.

The x value at the y axis would be $\displaystyle 0$.

 

[Deleted member 4993]

The x value at the y axis would be $\displaystyle 0$.

So put x =0 into your given equation and solve for y.

 

[Jason76]

So put x =0 into your given equation and solve for y.

Since it's a horizontal parabola, then it might come out to "two y intercepts" (assuming the vertex doesn't touch the y axis, or it isn't drawn away from the y axis). We can also say that it will NOT be a function.

 

[DrPhil]

Since it's a horizontal parabola, then it might come out to "two y intercepts" (assuming the vertex doesn't touch the y axis, or it isn't drawn away from the y axis). We can also say that it will NOT be a function.

What is "it"?
You are correct in saying y(x) is not a function.
However, x(y) is a perfectly well defined function that describes the parabola and its (two) intercepts.

 

[Jason76]

What is "it"?
You are correct in saying y(x) is not a function.
However, x(y) is a perfectly well defined function that describes the parabola and its (two) intercepts.

The "it" is the horizontal parabola which is NOT a function compared to the vertical one which is.

 

[HallsofIvy]

Strictly speaking, a parabola is a geometric set. It cannot be a function. What you mean is that the relation whose graph is the parabola is not a function. (Yes, that's a nitpick!)

 

[Jason76]

Strictly speaking, a parabola is a geometric set. It cannot be a function. What you mean is that the relation whose graph is the parabola is not a function. (Yes, that's a nitpick!)

A parabola could be described in two ways, horizontal or vertical, so you cannot say, generally, that it is a function. Right?

 

[lookagain]

A parabola could be described in two ways, horizontal or vertical, so you cannot say, generally, that it is a function. Right?

No, Jason76, I'll try to answer you using HallsofIvy's terms: A relation whose graph is a horizontal parabola is not a function. A relation whose graph is a vertical parabola is a function. Also, there are relations whose graphs are oblique parabolas.

 

[HallsofIvy]

I wouldn't say that a "parabola" is ever a "function"- it is a geometric object- that's what I said before. The equation describing a parabola is a function of a given variable. In a vertical parabola, of the form $\displaystyle y= a(x- b)^2+ C$, y is a function of x. In a horizontal parabola, of the form $\displaystyle x= a(y- b)^2+ c$, x is a function of y. There are, of course, parabolas that are neither "horizontal" nor "vertical", having axis of symmetry that makes a non-right angle with both x and y axes. In those cases, neither x nor y is a function of the other.