Question

Which equation reveals the minimum or the maximum value of f(x) without changing the form of the equation?

Answer 1

Answer:

A): f(x) = (x – 1)² + 2

Step-by-step explanation:

The quadratic function, f(x) = (x – 1)² + 2 is in vertex form: y = a(x - h)² + k, where:

• The vertex of the graph is (h,k).
• The value of a determines whether the graph opens up or down. If a is positive, the graph opens up and the vertex is its minimum point. If a is negative, then the graph opens down, and the vertex is its maximum point.
• The value of h determines how far left or right the parent function is translated.
• The value of k determines how far up or down the parent function is translated.

The function, f(x) = (x – 1)² + 2, provides the pertinent information that allows us to determine the parabola's minimum value, as the value of a is a positive, which implies that the parabola is upward facing, and the vertex, (1, 2) is the minimum point.

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