Here are the essential concepts you must grasp in order to answer the question correctly.
Quadratic Functions
A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax² + bx + c. In this case, the expression under the square root, 5x² - 10x + 5, is a quadratic function. Understanding its properties, such as the vertex, axis of symmetry, and roots, is essential for simplifying the function.
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Completing the Square
Completing the square is a method used to transform a quadratic expression into a perfect square trinomial. This technique allows for easier simplification and analysis of the function. By rewriting the quadratic in the form (x - p)² = q, we can simplify the expression under the square root and facilitate further calculations.
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Square Roots and Simplification
The square root function, denoted as √, is used to find a number that, when multiplied by itself, gives the original number. Simplifying expressions involving square roots often requires factoring out perfect squares or recognizing patterns. In this problem, simplifying √(5x² - 10x + 5) involves identifying and extracting any perfect square factors to express the function in a more manageable form.
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