The point (p, q) lies on the parabola y=ax2 . If you did not know the value of a, how could you use the values of p and q to determine whether the parabola is wider or narrower than y=x2? Use one example to describe.
To determine whether the parabola y=ax^2 is wider or narrower than the parabola y=x^2, we can compare the values of p and q.
The general form of the parabola y=x^2 is symmetric about the y-axis, with the vertex at (0, 0). This means that any point on the parabola can be expressed as (x, x^2) for some value of x.
Now, let's consider a specific example. Suppose we have a point (p, q) on the parabola y=ax^2. If the value of p is greater than 1, it means that the x-coordinate of the point is greater than 1. Thus, when compared to the parabola y=x^2, the point (p, q) is located further away from the y-axis. This indicates that the parabola y=ax^2 is wider than y=x^2.
For instance, let's take a = 1 and 2 as examples:
For the parabola y=x^2, the point (2, 4) lies on the curve.
For the parabola y=2x^2, the point (2, 8) lies on the curve.
Comparing these two points, we can see that the point (2, 8) is further away from the y-axis compared to (2, 4), indicating that the parabola y=2x^2 is wider than y=x^2.