Evaluate at \( t = 3 \): \( v(3) = 6(3)^2 - 10(3) + 4 = 54 - 30 + 4 = 28 \).
["Evaluate at ( t = 3 ): A Step-by-Step Guide to Solving the Expression", "Evaluating algebraic expressions at a specific value is a fundamental skill in mathematics, especially in algebra. In this article, we explore the evaluation of the expression\n[\nv(3) = 6(3)^2 - 10(3) + 4\n]\nand demonstrate exactly how to compute ( v(3) = 28 ), step by step.", "---", "### Understanding the Problem", "The expression ( v(t) = 6t^2 - 10t + 4 ) is defined for any value of ( t ). Here, we are asked to evaluate ( v ) at ( t = 3 ). This means replacing every instance of ( t ) in the expression with 3 and simplifying.", "---", "### Step 1: Substitute ( t = 3 ) into the Expression", "Start with:\n[\nv(3) = 6(3)^2 - 10(3) + 4\n]", "---", "### Step 2: Compute the Exponent", "[\n(3)^2 = 9\n]", "Now substitute:\n[\nv(3) = 6(9) - 10(3) + 4\n]", "---", "### Step 3: Perform Multiplication", "[\n6 \ imes 9 = 54\n]\n[\n10 \ imes 3 = 30\n]", "Now the expression is:\n[\nv(3) = 54 - 30 + 4\n]", "---", "### Step 4: Apply Addition and Subtraction Left to Right", "[\n54 - 30 = 24\n]\n[\n24 + 4 = 28\n]", "Thus, ( v(3) = 28 ).", "---", "### Final Result", "Evaluating the expression at ( t = 3 ) yields:\n[\n\boxed{v(3) = 28}\n]", "---", "### Why Evaluate at Specific ( t )?", "Calculating function values like ( v(3) ) is essential in calculus, modeling, and applied mathematics. It helps identify output values, find zeros, or analyze behavior across domains.", "---", "### Summary", "- Substitute ( t = 3 ) into the expression.\n- Simplify exponents, multiplication, and addition/subtraction step by step.\n- Careful computation ensures accurate results.\n- Example confirms: ( v(3) = 28 ).", "If you’re learning algebra or preparing for higher-level math, mastering function evaluation at specific values is a key step. Keep practicing—each computed value builds stronger mathematical confidence!", "---", "Keywords:\nevaluate algebraic expression at t=3, compute v(3), step-by-step algebra, solve 6(3)^2 -10(3)+4, math evaluation, quadratic function evaluation, calculus prep, algebra homework help, function value calculation."]
