Question

The vertex of a parabola is ( 3, -1). One point on the parabola is
( 6, 8) , find another point on the parabola.

Answer 1

Answer:

Step-by-step explanation:

If you plot the vertex and the point, you see that the point is above the vertex. Therefore, this is a positive parabola with the work form of

$y=a(x-h)^2+k$

We have values for x, y, h, and k. Let's write the equation of the parabola, put it into function notation, then find another x value at which to evaluate it.

$8=a(6-3)^2-1$ and

$8=a(3)^2-1$ and

8 = 9a - 1 and

9 = 9a so

a = 1. The equation of the parabola in function notation is

$f(x)=(x-3)^2-1$

Since the vertex is at (3, -1) it would make sense to evaluate the function at x values close to the vertex. Let's evaluate the function at an x value of 4:

$f(4)=(4-3)^2-1$ and

$f(4)=(1)^1-1$ and

f(4) = 0. That means that another point on this parabola will be (4, 0).