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Concept explainers
a.
To evaluate the domain of the function
a.
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Answer to Problem 79PFA
D. all real numbers
Explanation of Solution
Given information :
Quadratic function provided.
Options.
A.
B.
C.
D. all real numbers
The graph represented by the function is that of a parabola.
The domain of a quadratic function is
Option D. all real number; is the correct answer.
b.
To evaluate the range of the function
b.
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Answer to Problem 79PFA
A.
Explanation of Solution
Given information :
Quadratic function provided.
Options.
A.
B.
C.
D. all real numbers
Formula used :
Formula to compute the x-coordinate of the vertex is
Calculation :
Since the coefficient of ‘a’ is positive, the curve of this function is upward facing and hence the function has a minimum value.
x -coordinate of the vertex is
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
Simplifying
Vertex can be found out by putting the value of x computed in the axis of symmetry in the original function. This will give a value of y , that will be the minimum.
Putting the value of
Simplifying the expression.
Thus, the minimum is at
Since x can take up any real values, the domain is
Since the range is the values of y, it can only take up values greater than or equal to the minimum. That is,
Therefore, option A.
c.
To find the vertex of the function
c.
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Answer to Problem 79PFA
C.
Explanation of Solution
Given information :
Quadratic function provided.
Options.
A.
B.
C.
D.
Formula used :
Formula to compute the x-coordinate of the vertex is
Calculation :
Since the coefficient of ‘a’ is positive, the curve of this function is upward facing and hence the function has a minimum value.
x -coordinate of the vertex is
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
Simplifying
Vertex can be found out by putting the value of x computed in the axis of symmetry in the original function. This will give a value of y , that will be the minimum.
Putting the value of
Simplifying the expression.
Thus, the minimum is at
Hence the co-ordinates for the vertex are
Therefore, option C.
d.
To find the points that lie on the parabola
d.
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Answer to Problem 79PFA
C.
Explanation of Solution
Given information :
Quadratic function provided.
Options.
A.
B.
C.
D.
E.
F.
G.
Formula used :
The graph of a quadratic equation (
Calculation :
Option A.
Substituting
Putting the value of
Simplifying the expression.
Therefore,
The same method is followed for all the options to check if the point lies on the parabola.
Options:
B.
D.
E.
These three points are found to be on the parabola by the method mentioned above.
Chapter 9 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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