Question

lesson 23 - quadratic analysis with applications
score: 0/100 answered: 0/11
question 4
consider the function graphed at right.
the function has a select an answer of at ( x=)
the function is increasing on the interval(s):
the function is decreasing on the interval(s):
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Explanation:

Step1: Identify the vertex

The vertex of a parabola (quadratic function) is the point where it changes direction. For a parabola opening upwards (like the one in the graph), it has a minimum. From the graph, the vertex is at \(x = 1\) and \(y=-2\).

Step2: Determine increasing intervals

A function is increasing when the \(y -\)values rise as \(x -\)values increase. Looking at the graph, for \(x>1\), as \(x\) increases, \(y\) increases. Also, for \(x < - 1\), the function is increasing. So the increasing intervals are \((-\infty,-1)\cup(1,\infty)\)

Step3: Determine decreasing intervals

A function is decreasing when the \(y -\)values fall as \(x -\)values increase. From the graph, for \(-1

Answer:

The function has a minimum of \(-2\) at \(x = 1\).
The function is increasing on the interval(s): \((-\infty,-1)\cup(1,\infty)\)
The function is decreasing on the interval(s): \((-1,1)\)