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Through (-6, 8); perpendicular to 9x + 5y = 66. Write the equation in y = mx + b form.
1 answer:
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Part A) x-intercepts simply show that when the value of the function is zero. Vertex coordinates show that when the function obtains its maximum value. When x=50, function obtains its maximum value and it's 75. The function is increasing in the interval (0, 50) and decreasing in the interval (50, 100). In regard to the height and distance of the tunnel, these numbers show that decreasing and increasing intervals are symmetric. Each number from the intervals has its own pair in the corresponding interval and they are located in the same distance from the midpoint (50,75)
Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is
.
Plugging 15 and 35 in x, we can find the values of the function, i.e.
and 
.
Then, the average change is
Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is
Plugging 15 and 35 in x, we can find the values of the function, i.e.
Then, the average change is
Input (x-value)
Output (y-value)
You need to find the x-value that produces a y-value of -1. Since you know:
y = -1 Use the rule, and substitute/plug this into the equation
y = -2x + 33 Plug in -1 for "y" in the equation since y = -1
-1 = -2x + 33 Subtract 33 on both sides
-1 - 33 = -2x + 33 - 33
-34 = -2x Divide -2 on both sides to get "x" by itself
17 = x
An input of 17 yields an output of -1