Math Problem Statement
a quadratic parent function is vertically compresed by two thrids, reflected across the x axis, translated left three and up 7, write the equation in vertex form
Solution
To write the equation of the described quadratic function in vertex form, follow the steps:
Vertex form:
Where:
- determines the vertical stretch/compression and reflection.
- is the vertex of the parabola.
Step-by-step solution:
-
Start with the parent quadratic function:
-
Apply the vertical compression by :
-
Reflect across the x-axis (negate ):
-
Translate left by 3 units (replace with ):
-
Translate up by 7 units (add 7 to the entire equation):
Final equation in vertex form:
Would you like additional clarification or details? Here are 5 related questions to deepen your understanding:
- What would happen to the graph if the reflection across the x-axis was removed?
- How does a vertical compression differ from a vertical stretch?
- Can you describe the role of the vertex in the equation?
- What are some examples of transformations that don’t affect the vertex position?
- How would the equation change if the parabola was translated to the right instead of the left?
Tip: To visualize transformations, sketch each step incrementally to see how the graph evolves!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Transformations
Formulas
Vertex form of quadratic equation: y = a(x - h)^2 + k
Theorems
Transformation of quadratic functions
Suitable Grade Level
Grades 8-10