Concept explainers
For Exercises 1– 6, sketch the graph of each parabola. Determine the x- and y-intercepts, vertex, axis of symmetry, focus, and directrix for each.
To graph: The parabola
Explanation of Solution
Given:
The equation is
Graph:
To plot the graph of the function, consider the below mentioned steps and use the Ti-83 calculator:
The standard form of parabola
Step 1:
Press the [Y=] key to enter the equations for
Step 2:
Enter the equations in
Step 3:
Press [WINDOW] key to set the window and then edit the values as follows:
Step 4:
Press the [GRAPH] key to plot the graph.
Step 5:
Press the [TRACE] key to locate the intercept.
The graph thus obtained as follows:
The equation of the parabola
The y-intercept of the equation can be computed by putting the value of x equal to 0 as shown below:
Therefore, the y-intercept is
The x-intercept of the equation can be computed by putting the value of y equal to 0 as shown below:
Therefore, the x-intercepts are
The vertex in the equation of the parabola
Therefore the vertex of the equation is
The focus of the equation can be computed as
Since, in the equation
Therefore, focus can be written as
The directrix is
The axis of the symmetry for the equation
Hence, the x-intercepts are
Interpretation:
The x-intercepts are
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Chapter 7 Solutions
College Algebra (6th Edition)
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage