How do you solve for elimination method

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<span>The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation.</span>

<span>So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation. And since x + y = 8, you are adding the same value to each side of the first equation.</span>

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Answer the questions below about the quadratic function.f(x) = -2x² - 4x

Juli2301 [7.4K]

We are given the function below;

$f(x)=-2x^2-4x$

PART A

We then proceed to find if the function has a minimum or maximum value. To find if the function has a minimum or maximum value. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum.

ANSWER: From the above, we can see that x^2 is negative, hence the function has a maximum

PART B and C

To find the minimum or maximum value, we would plot the graph of the f(x). The graph can be seen below.

From the graph, the black point helps answer part A and part B.

ANSWER: The function's maximum value is f(x)=2.

This is the point where the slope of the graph is equal to zero

ANSWER: The maximum value then occurs at x= -1

We can also solve this by differentiating the function.

$\begin{gathered} f(x)=-2x^2-4x \\ f^{\prime}(x)=-4x-4 \\ At\xi maxmum\text{ }f^{\prime}(x)=0 \\ -4x-4=0 \\ -4x=4 \\ x=-\frac{4}{4} \\ x=-1 \\ \therefore\text{The max}imum\text{ value occurs at x=-1} \\ \text{Inserting the value of x into the function, we have} \\ f(x)=-2(-1)^2-4(-1) \\ f(x)=-2+4 \\ f(x)=2 \\ \therefore\text{The function max}imum\text{ value is 2} \end{gathered}$