Function Evaluation of f(x) = x^2

Math Problem Statement

Evaluate the function f(x) = x^2 - 10x + 4 for x = -2, -1, 0, 1, and 2, and complete the table.

Solution

The image you uploaded contains a table and an equation. The task involves evaluating the function $f(x) = x^2 - 10x + 4$ for different values of $x$ (-2, -1, 0, 1, 2), and completing the table.

Let me solve this step by step:

For $x = -2$ :

$f(-2) = (-2)^2 - 10(-2) + 4 = 4 + 20 + 4 = 28$
For $x = -1$ :

$f(-1) = (-1)^2 - 10(-1) + 4 = 1 + 10 + 4 = 15$
For $x = 0$ :

$f(0) = (0)^2 - 10(0) + 4 = 0 + 0 + 4 = 4$
For $x = 1$ :

$f(1) = (1)^2 - 10(1) + 4 = 1 - 10 + 4 = -5$
For $x = 2$ :

$f(2) = (2)^2 - 10(2) + 4 = 4 - 20 + 4 = -12$

Thus, the completed table looks like this:

\hline x & -2 & -1 & 0 & 1 & 2 \\ \hline y & 28 & 15 & 4 & -5 & -12 \\ \hline \end{array}$$ Would you like further details on the steps or have any questions? Here are 5 additional questions related to this topic: 1. How does the function behave when $$x$$ increases or decreases? 2. What is the vertex of the quadratic function? 3. How would you find the roots of the quadratic equation $$f(x) = 0$$? 4. How does the coefficient of $$x^2$$ affect the graph of the function? 5. Can this function represent a real-world situation? How would you interpret the coefficients? Tip: Always remember to expand and simplify each term carefully when solving quadratic equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Function Evaluation

Formulas

Quadratic function formula: f(x) = ax^2 + bx + c

Theorems

Suitable Grade Level

Grades 8-10

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