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Identify the family of curves represented by the equation y = ax^2 + bx + c.
Identify the family of curves represented by the equation y = ax^2 + bx + c.
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Practice Questions
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Q1
Identify the family of curves represented by the equation y = ax^2 + bx + c.
Linear functions
Quadratic functions
Cubic functions
Exponential functions
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The equation y = ax^2 + bx + c represents a family of quadratic functions with varying coefficients (a, b, c).
Questions & Step-by-step Solutions
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Q: Identify the family of curves represented by the equation y = ax^2 + bx + c.
Solution:
The equation y = ax^2 + bx + c represents a family of quadratic functions with varying coefficients (a, b, c).
Steps: 5
Show Steps
Step 1: Understand that the equation y = ax^2 + bx + c is a mathematical expression.
Step 2: Recognize that 'a', 'b', and 'c' are constants that can change.
Step 3: Note that 'a' determines the shape of the curve (whether it opens up or down).
Step 4: Understand that 'b' and 'c' affect the position of the curve on the graph.
Step 5: Realize that changing 'a', 'b', or 'c' creates different curves, but they all belong to the same family called quadratic functions.
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