Write the equation of the quadratic function with roots 0 and 2 and a vertex at (1, 5).

The "standard" parabola with roots 0 and 2 is

All multiples of this parabola, i.e.

have the same roots. We can choose the factor such that the parabola passes through the desided point: if we plug 1, 5 for x, y we have

So, our claim is that the parabola

has roots 0 and 2 and vertex at (1, 5).

You can easily verify this: the roots are guaranteed by the fact that we can write the equation as

The vertex must be at x=1, because it's the midpoint of the roots. Moreover, if we evaluate the function at x=1 we have

as required.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.