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2 years ago

Evaluate the function f(x) = - 2x^2 + 2x + 4 Find f(1)

Mathematics

1 answer:

AlekseyPX2 years ago

6 0

Answer:

f(1) = 4

Step-by-step explanation:

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

f(1) = - 2(1)^2 + 2(1) + 4

f(1) = -2 + 2 + 4

f(1) = 4

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Solution

- The solution steps are given below:

$\begin{gathered} \text{ Let the original amount be X} \\ \\ \text{ If we want a 28\% raise over the next two years, then it means that the amount will be:} \\ X+\frac{28}{100}X=1.28X \\ \\ \text{ If we want to give them a consistent raise each year, we can compute the scenario as follows:} \\ \text{ Let the percentage be }y \\ \\ X+y\%\text{ of }X=\text{ Salary after first year} \\ \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)\text{ = Salary after second year.} \\ \\ \text{ But we already know that the salary after second year is }1.28X \\ \text{ Thus, we can say:} \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)=1.28X \\ \\ \text{ Simplifying, we have:} \\ X+\frac{yX}{100}+\frac{y}{100}(X+\frac{yX}{100})=1.28X \\ \\ \text{ Divide through by }X \\ 1+\frac{y}{100}+\frac{y}{100}(1+\frac{y}{100})=1.28 \\ \\ \text{ Subtract 1 from both sides and expand the brackets} \\ \frac{y}{100}+\frac{y}{100}+(\frac{y}{100})^2=1.28-1=0.28 \\ \\ \frac{2y}{100}+(\frac{y}{100})^2=0.28 \\ \\ \text{ Multiply both sides by }100^2 \\ 200y+y^2=2800 \\ \\ \text{ Rewrite, we have:} \\ y^2+200y-2800=0 \\ \\ Solving\text{ the equation using the Quadratic formula, we have that:} \\ y=\frac{-200\pm\sqrt{200^2-4(-2800)}(1)}{2(1)} \\ \\ y=-213.137\text{ or }13.137 \\ \\ \text{ Since the change in salary is an increase, thus, the rate }y\text{ has to be positive.} \\ \text{ Thus, } \\ y=13.137\approx13.14\% \\ \\ \end{gathered}$

Final Answer

y = 13.14%

The screenshots of the solution are:

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