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To find the gradient of the tangent, we must first differentiate the function.

The gradient at x = 0 is given by evaluating f'(0).

The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.
The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

So the point (0, -1) lies on the tangent. Substituting into the tangent equation:
The answer is 3/5.

Continue this pattern and you'll see that it follows this geometric sequence

The given two polygons are similar to one another ~
Sides of the given polygons are in ratio of :

to put in simple Ratio ~

So, the sides of the larger polygon are :
Now, to find the Perimeter of larger polygon ~ add the side length of all sides :


Answer:

Step-by-step explanation:
step 1
we have the points
(-1,0), (-2,0), and (0,2)
Plot the points
using a graphing tool
see the attached figure
The graph of a quadratic function must be a vertical parabola open upward
The vertex is a minimum
The quadratic function in general form is equal to

Substitute the value of x and the value of y of each given ordered pair in the general equation and solve for a,b and c
(0,2)
For x=0, y=2
substitute

(-1,0)
For x=-1, y=0
substitute

---->
----> equation A
(-2,0)
For x=-2, y=0
substitute

----> equation B
we have the system
----> equation A
----> equation B
substitute equation A in equation B
solve for b

Find the value of a
therefore
The quadratic function in general form is equal to

see the attached figure N 2 to better understand the problem