Question 4 of 10
2 answers:
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Answer:
Step-by-step explanation:
<u>System Of Linear Equations </u>
In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.
We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)
The general quadratic function can be written as
We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1
Now we use the second condition f(1)=5
Finally, we use the third condition f(2)=10
We put together eq 1, eq 2, and eq 3 to form the system
Adding the first two equations we have
And also
Using the above equation and the value of b in the third equation, we have
Subtracting the first equation from the second
And therefore
Now we have all the values, the quadratic function is
For this case we have the following function:
To find the maximum of the function, what we should do is to derive the equation.
We have then:
We match zero:
We clear the value of x:
We substitute the value of x in the function to find the maximum:
Rewriting:
Answer:
a formula in terms of a for the maximum of f (x) is:
To find the maximum of the function, what we should do is to derive the equation.
We have then:
We match zero:
We clear the value of x:
We substitute the value of x in the function to find the maximum:
Rewriting:
Answer:
a formula in terms of a for the maximum of f (x) is: