if the table of the function contains exactly two potential turning - points, one with an input value of…

if the table of the function contains exactly two potential turning - points, one with an input value of - 1, which statement best describes all possible values of m?\n-3 -12\n-2 m\n-1 4\n0 0\n1 -4\n2 -2\nm ≥ - 12\n-12 < m < 4\nm ≤ 4\nm ≥ 4 or m ≤ - 12

if the table of the function contains exactly two potential turning - points, one with an input value of - 1, which statement best describes all possible values of m?\n-3 -12\n-2 m\n-1 4\n0 0\n1 -4\n2 -2\nm ≥ - 12\n-12 < m < 4\nm ≤ 4\nm ≥ 4 or m ≤ - 12

Answer

Explanation:

Step1: Understand turning - point concept

A turning point of a function is a point where the function changes from increasing to decreasing or vice - versa.

Step2: Analyze the given values

We know that one turning point is at (x = - 1) with (f(-1)=4). For there to be exactly two turning points, the value of (m = f(-2)) must be such that the function changes direction appropriately. If (m\geq4) or (m\leq - 12), the function will have the required two turning points. If (-12 < m<4), there may not be two distinct turning points as the function may not change direction in the right way.

Answer:

(m\geq4) or (m\leq - 12)