Questions: QUESTION 3 Given: f(x)=-3 x^2-x+2, find f(-1/2) 7/4 9/4 13/4 None of the above

QUESTION 3 Given: f(x)=-3 x^2-x+2, find f(-1/2) 7/4 9/4 13/4 None of the above
Transcript text: QUESTION 3 Given: $f(x)=-3 x^{2}-x+2$, find $f\left(-\frac{1}{2}\right)$ $\frac{7}{4}$ $\frac{9}{4}$ $\frac{13}{4}$ None of the above
failed

Solution

failed
failed

Solution Steps

To find \( f\left(-\frac{1}{2}\right) \) for the function \( f(x) = -3x^2 - x + 2 \), substitute \( x = -\frac{1}{2} \) into the function and simplify the expression to find the value.

Step 1: Substitute \( x = -\frac{1}{2} \) into the function

Given the function \( f(x) = -3x^2 - x + 2 \), we need to find \( f\left(-\frac{1}{2}\right) \). Substitute \( x = -\frac{1}{2} \) into the function:

\[ f\left(-\frac{1}{2}\right) = -3\left(-\frac{1}{2}\right)^2 - \left(-\frac{1}{2}\right) + 2 \]

Step 2: Simplify the expression

Calculate each term separately:

  1. \(-3\left(-\frac{1}{2}\right)^2 = -3 \times \frac{1}{4} = -\frac{3}{4}\)
  2. \(-\left(-\frac{1}{2}\right) = \frac{1}{2}\)
  3. The constant term is \(2\).

Combine these results:

\[ f\left(-\frac{1}{2}\right) = -\frac{3}{4} + \frac{1}{2} + 2 \]

Step 3: Perform the arithmetic

Convert all terms to a common denominator and add them:

\[ f\left(-\frac{1}{2}\right) = -\frac{3}{4} + \frac{2}{4} + \frac{8}{4} = \frac{7}{4} \]

Final Answer

\(\boxed{\frac{7}{4}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Solve the given inequality. Write the solution set using interval notation, then graph it. (5-2x)/5 ≥ -2 The solution set is (Simplify your answer. Type your answer in interval notation.)
failedAnswered
Use the given graph to estimate the value of each derivative. (i) (a) f'(0) (b) f'(1) (c) f'(2) (d) f'(3) (e) f'(4) (f) f'(5)
failedAnswered
Hints The knee is proximal to the ankle. Which of these other terms could also be used to correctly describe the relationship between the knee and the ankle? The knee is contralateral to the ankle. The knee is medial to the ankle. The knee is superficial to the ankle. The knee is superior to the ankle. Hints Clear all Check answer
failedAnswered
Find the surface area of a cylinder with a base diameter of 10 ft and a height of 7 ft. Write your answer in terms of π, and be sure to include the correct unit.
failedAnswered
Budgeting Decision Point Managers - Google Chrome pe-xl-prod.knowdl.com/content/qualsims/accounting/budgetingsim/v2/player/#/265d911b8dd98f8f2e9d60cac9346771qualsimsaccountingbudgetingsimmillernoblesmattison7/ Decision Point: Managers Timing for your budgeting process review, including a draft of comprehensive first quarter budgets, should not be a constraint since you are only at the halfway point in the current fiscal year when you kick off your review. That being said, you can't get very far until the team determines who should be involved in the budgeting process. Which managers should participate in the budgeting process? Select an option from the choices below and click Submit. Top-level managers only since they establish the company's goals and formulate business strategies. This top-down approach for establishing the budget will ensure company resources are in line with the long-term strategic plans. Include all levels of management since managers will be more motivated by the budgets if they have a say in creating them.