39.2k views
0 votes
Given the function f(x)=x2−3x+2:

a. To find f(4), substitute x=4 into the function: f(4)=42−3(4)+2=16−12+2=6
b. To find f(−3), substitute x=−3 into the function: f(−3)=(−3)2−3(−3)+2=9+9+2=20
c. f(a)=a2−3a+2

User Zuberuber
by
8.2k points

1 Answer

5 votes

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.

User Bill Barnhill
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories