Write the standard form of the equation of the parabola whose vertex is 1,2 and passes through the point 0,0. The answer according to my book is 0=a(0-1)^2+2. But which 0 in the equation is the first 0 fromn (0,0) and which one is the second? Thanks!

In the equation 0 = a(0-1)^2 + 2, the first 0 represents the y-coordinate of the point (0,0), and the second 0 represents the value of the quadratic function when x = 0.

To understand why this is the case, let's break down the equation and its components:

1. The equation of a parabola in standard form is given by:
y = a(x-h)^2 + k,
where (h, k) is the vertex of the parabola.

2. In this case, the vertex is given as (1,2), so we substitute h=1 and k=2 into the equation:
y = a(x-1)^2 + 2.

3. We know that the parabola passes through the point (0,0). To find the corresponding value of a, we substitute x=0 and y=0 into the equation:
0 = a(0-1)^2 + 2.

By substituting the given values, we have effectively plugged in (0,0) into the equation. The first 0 in the equation represents the y-coordinate of the point (0,0), which is 0. The second 0 in the equation represents the value of y when x=0, which we set to 0 because the point (0,0) lies on the parabola.

Therefore, the completed equation is 0 = a(0-1)^2 + 2, and solving this equation will allow you to find the corresponding value of a.