Is the graph of a parabola a function? I say that it is a function.
only if its axis of symmetry is a vertical line
The graph of the parabola lays on it side with the x-axis dividing the parabola.
So following the answer that I gave you above, what do you think?
I say yes.
Yes, the graph of a parabola is indeed a function. In order to understand why, let's first define what it means for a graph to be a function.
A function is a mathematical rule that assigns exactly one output value for each input value. In other words, if you have a set of input values, each input value can only correspond to one output value.
Now, let's consider the graph of a parabola. A parabola is a U-shaped curve that can either open upwards or downwards, depending on its equation. The general equation of a parabola is given by y = ax^2 + bx + c, where a, b, and c are constants.
When we graph a parabola, we plot points that satisfy this equation. For any given x-value, there can be only one corresponding y-value. This is because each x-value is squared, and squaring any real number always gives a unique result. Therefore, the graph of a parabola passes the vertical line test, meaning that every vertical line that intersects the graph does so in at most one point.
Hence, since the graph of a parabola satisfies the criteria of a function, it is indeed a function.