Question

Is a parabola a function?

Answer 1

Checking if a parabola is a function

The graph of a parabola is a U-shaped curve that opens upward or downward.

It is written in the form $a{x}^2+bx+cwherea,b,c$ are real numbers and $a\ne 0.$ it is also the form of a quadratic equation. Any quadratic function's graph is always that of a parabola.

We can also check this with the help of a vertical line test. According to the vertical line test, if a vertical line cuts the graph more than once then for every $x-value$ there is no unique $y-value$. Therefore, the relation is not a function.

Considering the case of a parabola we see, that the vertical line cuts the graph only once, so the vertical test qualifies and hence, a parabola is a function.

Thus, a parabola is a function.