Hello! Please explain how to solve this step-by-step. (Question 111.) I tried solving but not sure if I did it correctly. Thanks!

Step-by-step explanation:

We want to find the equation of a parabola of the form:

This passes through (0,1) and is tangent to the line:

At the point (1,0).

First, note that (0,1) is the y-intercept. In other words, our constant c is 1. Thus:

From the equation of the tangent line, we can see that it has a slope of one.

Recall that the slope of the tangent line at a point is equivalent to the value of the derivative at the same point.

In other words, the value of the derivative of our parabola at x = 1 must be one.

Find the derivative. Take the derivative of both sides with respect to x:

Expand:

Use the Power Rule. Since we're differentiating with respect to x, we can treat a and b as constants. Thus:

Now, since the slope of the tangent line at x = 1 is 1, this means that:

Simplify:

Let's hold on to this equation for now.

Since the line is tangent at the point (1,0), this means that our original function equals zero when x = 1. In other words:

Simplify:

This yields the following system of equations:

Solve for a and b.

From our previous equation, let's subtract 2a from both sides:

Substitute this into the newly acquired equation:

Solve for a. Rewrite:

Combine like terms:

Hence:

Find b:

Therefore, a = 2 and b = -3.

Then by substitution, we can see that our final equation is:

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)

figure c

step-by-step explanation:

hope this .