functions f(x) and g(x) with given equations, we'll use the vertex form of a quadratic equation: y = a (x - h)² + k. Assuming we have the equations for f(x) and g(x), let's proceed step by step:
functions f(x) and g(x) with given equations, we'll use the vertex form of a quadratic equation: y = a (x - h)² + k. Assuming we have the equations for f(x) and g(x), let's proceed step by step:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
“Sketch both of the functions and on a single xy-plane. Describe the steps you took to create your sketch. “ I have the instructions on how to do it. I just need someone to answer the question!
Transcribed Image Text:functions f(x) and g(x) with given equations,
we'll use the vertex form of a quadratic
equation: y = a(x – h)² + k. Assuming we
have the equations for f (x) and g(x), let's
proceed step by step:
1. Identify the Equations: First, we need the
specific equations for f(x) and g(x). For
example, let's assume:
• ƒ(x) = 2(x − 3)² + 4
●
' g(x) = −1(x + 1)² + 7
These equations represent the two functions
in vertex form.
2. Identify the Vertex: From the equations, we
can identify the vertex for each parabola:
For f(x), the vertex is at (3, 4).
• For g(x), the vertex is at (−1, 7).
3. Determine the Axis of Symmetry: The axis of
symmetry is the vertical line through the
vertex. It's the equation x = = h, where h is the
●
x-Coordinate of the vertex
Transcribed Image Text:For f(x), the axis of symmetry is x
=
• For g(x), the axis of symmetry is x = −1.
4. Plot the Vertex: On your xy-plane, mark the
vertex for each function. For f(x), plot the
point (3, 4), and for g(x), plot the point (-1, 7).
5. Determine the Direction of Opening: Look at
the "a" value in each equation. If "a" is positive,
the parabola opens upward; if "a" is negative,
it opens downward.
For f(x), with a = 2, the parabola opens
upward.
• For g(x), with a = -1, the parabola
opens downward.
3.
6. Plot Additional Points: To complete the
graphs, you can plot a few more points
symmetrically on each side of the vertex.
For f(x), you can choose x-values like 2,
4, 5, etc., and calculate the corresponding
●
y-values using the equation.
• For a(x) you can choose v-valuos liko -2
Expert Solution
Step 1: Definition
The equation of parabola is of the form
- Vertex :
- Axis of symmetry :
- If a>0 , then parabola opens upward .
- If a<0 , then parabola opens downward.
Step by step
Solved in 3 steps with 2 images
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