Math Problem Statement

Evaluate the function f(x) = x^2 + 3x - 4 at specific values: f(2), f(-3), f(0).

Solution

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The text from the image appears to focus on evaluating the function f(x)=x2+3x4f(x) = x^2 + 3x - 4 at specific values of xx:

  1. f(2)f(2)
  2. f(3)f(-3)
  3. f(0)f(0)

Let's solve each one:

  1. Evaluate f(2)f(2):

    Substitute x=2x = 2 into the function f(x)=x2+3x4f(x) = x^2 + 3x - 4: f(2)=(2)2+3(2)4=4+64=6f(2) = (2)^2 + 3(2) - 4 = 4 + 6 - 4 = 6 So, f(2)=6f(2) = 6.

  2. Evaluate f(3)f(-3):

    Substitute x=3x = -3 into the function f(x)=x2+3x4f(x) = x^2 + 3x - 4: f(3)=(3)2+3(3)4=994=4f(-3) = (-3)^2 + 3(-3) - 4 = 9 - 9 - 4 = -4 So, f(3)=4f(-3) = -4.

  3. Evaluate f(0)f(0):

    Substitute x=0x = 0 into the function f(x)=x2+3x4f(x) = x^2 + 3x - 4: f(0)=(0)2+3(0)4=0+04=4f(0) = (0)^2 + 3(0) - 4 = 0 + 0 - 4 = -4 So, f(0)=4f(0) = -4.

Summary:

  • f(2)=6f(2) = 6
  • f(3)=4f(-3) = -4
  • f(0)=4f(0) = -4

Would you like more details or have any questions about these calculations?

Related Questions:

  1. What is the general process for evaluating any function f(x)f(x) at a given value of xx?
  2. How would the graph of f(x)=x2+3x4f(x) = x^2 + 3x - 4 look?
  3. What are the roots of the equation x2+3x4=0x^2 + 3x - 4 = 0?
  4. How does the sign of the coefficient of x2x^2 affect the shape of the parabola for a quadratic function?
  5. What are the vertex and axis of symmetry of the function f(x)=x2+3x4f(x) = x^2 + 3x - 4?

Tip:

When evaluating a function at a specific point, always ensure that you carefully substitute the value into the equation and simplify step by step to avoid mistakes.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Function Evaluation

Formulas

f(x) = ax^2 + bx + c
Substitution Method

Theorems

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Suitable Grade Level

Grades 7-9