Final answer:
The question involves evaluating a quadratic function, using the quadratic formula, 'undoing' squares with square roots, understanding constant functions within a range, and handling operations with signed numbers.
Step-by-step explanation:
The question pertains to evaluating a quadratic function f(x) = x² - 3x + 2 at specific values and understanding operations with functions and quadratic equations. For example, to compute f(4), you substitute 4 into the function to get f(4) = 4² - 3(4) + 2, which simplifies to 6. Similarly, substituting x = -3 yields f(-3) = (-3)² - 3(-3) + 2, simplifying to 20.
When working with quadratic equations like ax² + bx + c = 0, the quadratic formula is used to find the solutions: x = (-b ± √(b² - 4ac)) / (2a). If a problem involves 'undoing' a square, such as finding the side length of a right triangle (applying the Pythagorean Theorem), you take the square root of both sides after isolating the squared term.
For functions that are constant within a range, such as f(x) = 20 for 0 ≤ x ≤ 20, f(x) remains the same value within that range, resulting in a horizontal line segment on the graph.
Determining the behavior of functions at specific points, like y = 13x or y = x² at x = 3, involves analyzing the function value and its slope. In addition, operations with signed numbers, such as 5 - (+3), are simplified by changing the operation according to the rules of signed numbers, resulting in 5 - 3, which equals 2.