Math Problem Statement

f(6)=−3x2+6x+1,

Solution

It seems you want to evaluate the function f(x)=3x2+6x+1f(x) = -3x^2 + 6x + 1 at x=6x = 6.

Let's calculate f(6)f(6):

f(6)=3(6)2+6(6)+1f(6) = -3(6)^2 + 6(6) + 1

First, calculate 626^2:

62=366^2 = 36

Now multiply by 3-3:

3×36=108-3 \times 36 = -108

Next, calculate 6×66 \times 6:

6×6=366 \times 6 = 36

Now, add these results together along with the constant term 11:

f(6)=108+36+1=71f(6) = -108 + 36 + 1 = -71

So, f(6)=71f(6) = -71.

Would you like more details on this calculation, or do you have any other questions?

Here are 5 related questions to consider:

  1. How would you find the roots of the function f(x)=3x2+6x+1f(x) = -3x^2 + 6x + 1?
  2. What is the vertex of the parabola represented by the function f(x)=3x2+6x+1f(x) = -3x^2 + 6x + 1?
  3. How does changing the coefficient of x2x^2 in the function f(x)f(x) affect the shape of the parabola?
  4. Can you determine the axis of symmetry for the function f(x)=3x2+6x+1f(x) = -3x^2 + 6x + 1?
  5. What is the y-intercept of the function f(x)=3x2+6x+1f(x) = -3x^2 + 6x + 1?

Tip: When evaluating a function, always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

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Math Problem Analysis

Mathematical Concepts

Quadratic Equations
Function Evaluation
Order of Operations

Formulas

Quadratic equation formula ax^2 + bx + c
Order of operations (PEMDAS)

Theorems

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Suitable Grade Level

Grades 9-12