To select the statement which best describes the function.
Answer to Problem 13PFA
Option D. In standard form, the equation of the function is
Explanation of Solution
Given information :
Graph representing the function
Option A.
Option B.
Option C. In vertex form, the equation of the function is
Option D. In standard form, the equation of the function is
:
Option A.
It is difficult to conclude from the given graph if it is indeed vertically compressed.
Therefore, option A is rejected as it does not describe the graph of
Option B.
The graph of a quadratic equation (
This vertex point shall be:
Highest point (if
Or, lowest point (if
In this case, ‘a’ is greater than 0 hence the graph will have a minimum and will open upwards.
A parabola always points to infinity, either negative or positive.
Therefore, option B is rejected as it is incorrect.
Option C. In vertex form, the equation of the function is
The graph of quadratic function
If
If
The graph represented by is equivalent to the graph of that has been translated vertically. The direction of translation or movement of the graph is dependent on the value of k .
If the graph of is translated units upwards.
If the graph of is translated units downwards.
The graph represented by is equivalent to the graph of that has been translated horizontally. The direction of translation or movement of the graph is dependent on the value of
If the graph of is translated units to the right.
If the graph of is translated units to the left.
Therefore, as seen in the graph there is a vertical translation downwards by 6 units, a horizontal translation to the right by 2 units and a vertical stretch by a factor of 2.
Hence, option C is selected as the correct option describing the graph in the best way possible.
Option D. In standard form, the equation of the function is
Substituting in the expression above.
Simplifying.
ThusAccording to the graph this value should be
Therefore, option D. can be rejected.
Chapter 9 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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