What is the equation of a parabola that never crosses the y-axis?

Question

My teacher said that this might involve some calculus or something. Also I am currently taking Algebra II and Intro to Geometry.

Answer 1

An equation for a parabola that never crosses the y-axis would be one the either opens to the left or right (i.e., it's turned on its side). An example equation of this type of parabola would be x = y²+1 . I would encourage you to try typing this equation into a graphing calculator (or, if you don't have one, follow this link: https://www.desmos.com/calculator ) just so you can see what it looks like.

If you have any questions, please don't hesitate to reach out!

Answer 2

An equation that opens along the x axis, that does cross the y axis including the point (0,0)

Typically equations of parabolas are given in vertex or standard form along the y axis

y = a(x -h)² + k

Or

y =ax²

y = ax² + bx + c

Symmetry would suggest that you can switch the x and y roles but one must keep in mind the vertex (h,k) and focus (h + a, k) and directrix equal to x = h - a ; along the x axis

Along the x axis

x = a(y - k)² + h

Graph

x = 3a(y - k)² + h

vertex (1,1), passing through point (4,0), (4, 2), by the way a= 1

Try graphing an

x = y² + by + c

x = y² + 6 + 13

Compared to

x = 8y² -16y + 9

OR

x = y² + 6y + 9

You can use a graphing calculator or graph at Desmos.com

Since you are in Algebra 2, you can also set out to take the vertex form

y = a(x - h)² + k

and solve it for x instead of y, depending on how far along you are in class you can see how the variables move around for example you would start with

y - k = a(x - h)²

You can also look this up.

Answer 3

y = x^2+3

y = x^2 + k where k>0