Concept explainers
To formulate an equation for the graph shown.
Answer to Problem 70HP
The
Explanation of Solution
Given information :
The given figure shows a downward facing parabola.
Vertex of the graph is at
y-intercept is
Hence, the axis of symmetry is
x-intercept is
Formula used :
The graph of a quadratic equation (
The axis of symmetry bisects the parabola into two equal parts. Hence each point on the parabola would have an equal point on the other side of the axis of symmetry
This vertex point shall be:
Highest point (if
Or, lowest point (if
In this case, ‘a’ is lesser than 0 hence the graph will have a maximum and will open downwards.
A parabola always points to infinity, either negative or positive.
Formula to compute equation of the axis of symmetry
Axis of symmetry is
Calculation :
Equating the two equations above.
Simplifying the expression.
In the above expression
Putting
In quadratic form,
Here, c is the y-intercept.
Putting
Simplifying.
This corresponds to the x-intercept
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Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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