Find the quadratic function that fits curve below. Select the correct answer.
1 answer:
<h2>Hello!</h2>
The answer is:
The quadratic function that fits the given picture is:
We can solve the problem and find the correct function that fits the curve below by finding which function intercepts the y-axis at -5 (we can see it from the picture), also, we need to look for a function that represents a parabola opening upwards. We need to remember that when a parabola is opening upwards, its quadratic term coefficient is negative.
So, we can see that from the given functions, the only function that represents a parabola opening upwards and its y-intercept is located at y equal to -5 is the second option:
We have that :
We can see that the quadratic term (a) is negative, and the quadratic function intercepts the y-axis at y equal to -5.
Hence, the answer is:
The quadratic function that fits the given picture is:
Have a nice day!
Note: I have attached a picture for better understanding.
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Answer:
The bounded area is:
Step-by-step explanation:
Let's start by plotting the functions that enclose the area, so we can find how to practically use integration. Please see attached image where the area in question has been highlighted in light green. The important points that define where the integrations should be performed are also identified with dots in darker green color. These two important points are: (2, 6) and (3, 1)
So we need to perform two separate integrals and add the appropriate areas at the end. The first integral is that of the difference of function y=x+4 minus function y=(1/3)x , and this integral should go from x = 0 to x = 2 (see the bottom left image with the area in red:
The next integral is that of the difference between and the bottom line defined by: y = (1/3) x. This integration is in between x = 2 and x = 3 (see bottom right image with the area in red:
Now we need to add the two areas found in order to get the total area:
