1. Identify the Vertex: From each equation, find the vertex. The vertex is the point (h, k) where: • For f(x): h = 3 and k = 4. • For g(x): h = -1 and k = 7. : 2. Determine the Direction of Opening: Check the "a" value in each equation: For f(x): a = 2, so it opens upward. • For g(x): a 3. Plot the Vertex: On your xy-plane, mark the vertex for each function: • For f(x): Plot the point (3, 4). ● • For g(x): Plot the point (-1, 7). 4. Identify the Axis of Symmetry: The axis of symmetry is a vertical line through the vertex. It's x = h: For f(x): Axis of symmetry is x = 3. • For g(x): Axis of symmetry is – 1. 5. Plot Additional Points: To complete the graphs, choose some x-values on each side of ● ● - -1, so it opens downward. =
1. Identify the Vertex: From each equation, find the vertex. The vertex is the point (h, k) where: • For f(x): h = 3 and k = 4. • For g(x): h = -1 and k = 7. : 2. Determine the Direction of Opening: Check the "a" value in each equation: For f(x): a = 2, so it opens upward. • For g(x): a 3. Plot the Vertex: On your xy-plane, mark the vertex for each function: • For f(x): Plot the point (3, 4). ● • For g(x): Plot the point (-1, 7). 4. Identify the Axis of Symmetry: The axis of symmetry is a vertical line through the vertex. It's x = h: For f(x): Axis of symmetry is x = 3. • For g(x): Axis of symmetry is – 1. 5. Plot Additional Points: To complete the graphs, choose some x-values on each side of ● ● - -1, so it opens downward. =
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The question is: “Sketch both of the functions and on a single xy-plane. Describe the steps you took to create your sketch.” Below i have pictures of the functions and there values to be graphed. a please do this! using the notes recorded below. Please graph!
Transcribed Image Text:1. Identify the Vertex: From each equation, find
the vertex. The vertex is the point (h, k)
where:
• For f(x): h = 3 and k = 4.
• For g(x): h = -1 and k = 7.
2. Determine the Direction of Opening: Check
the "a" value in each equation:
• For f(x): a = 2, so it opens upward.
For g(x): a
3. Plot the Vertex: On your xy-plane, mark the
vertex for each function:
For f(x): Plot the point (3, 4).
For g(x): Plot the point (-1, 7).
4. Identify the Axis of Symmetry: The axis of
symmetry is a vertical line through the vertex.
●
●
It's x
=
●
:h:
=
-1, so it opens downward.
For f(x): Axis of symmetry is x
=
For g(x): Axis of symmetry is a = −1.
5. Plot Additional Points: To complete the
graphs, choose some x-values on each side of
3.
the vortov and calculate the corresponding v-
Transcribed Image Text:5. Plot Additional Points: To complete the
graphs, choose some x-values on each side of
the vertex, and calculate the corresponding y-
values using the equations.
For f(x): Choose x-values like 2, 4, 5, etc.,
and calculate y-values using the equation.
• For g(x): Choose x-values like -2, -3, 0,
etc., and calculate y-values.
6. Draw the Parabolas: Connect the plotted
points to create the parabolic shapes. Ensure
that the direction of opening (upward or
downward) aligns with the "a" value in each
equation.
By following these simplified steps and using
the specific equations and values, you can
accurately sketch the graphs of f(x) and
g(x) on the same xy-plane.
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