To state if the statement is true or false
Answer to Problem 22E
True
Explanation of Solution
Given information:
A statement saying “The graph of a quadratic model with a negative leading coefficient will have a maximum value at its vertex”.
A mathematical model represented by
The, leading coefficient of the quadratic equation
The maximum value of a function is a point where a function reaches its highest point on the graph.
Given that, the quadratic model has a negative leading coefficient.
When a graph is drawn with above conditions of quadratic equation, there will be two cases.
Case (i):
The above figure shows that the parabola is opened leftwards whose equation is
The maximum point of the parabola is at the point
Even if the value of h and k increases the maximum point lies in the right side of the
Case (ii):
The above figure shows that the parabola is opened downwards whose equation is
The maximum point of the parabola is at the point
Even if the value of h and k increases the maximum point lies on the left side of the
So, the graph of a quadratic model with negative leading coefficient will have a maximum value at its vertex.
Chapter 2 Solutions
Precalculus with Limits: A Graphing Approach
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