Calculate the rate of change for the quadratic function over the given interval: f(x)=x^2 + 4x +5 ; -4 =< x =< -2

The average rate of change for this quadratic function is -2.

Step-by-step explanation:

In this question, we have f(x) = y = x^{2} + 4x + 5.

Given a function y, the average rate of change S of y=f(x) in an interval  [x_s, x_f] will be given by the following equation:

S = \frac{f(x_{f}) - f(x_s)}{x_f - x_s}

So, in  your problem, f(x) = x^{2} + 4x + 5, x_{f} = -2 and x_{s} = -4.

Applying these informations to the equation S above, we have:

S = \frac{f(-2) - f(-4)}{-2-(-4)}

Where

f(-2) = (-2)^{2} + 4(-2) +5 = 4-8+5 = 9-8 = 1

f(-4) = (-4)^{2} + 4(-4) +5 = 16-16+5 = 5

So, the average rate of change S will be

S = \frac{1-5}{2} = -4

-232

step-by-step explanation:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3