Math Problem Statement
y=1/4x² +x-6 graph these equationns identify the axis of symmetry vertex and y intercept
Solution
To analyze and graph the quadratic equation , we need to determine the axis of symmetry, vertex, and y-intercept.
Step 1: Rewrite the equation in standard form
The given equation is already in the standard form:
Here:
Step 2: Axis of Symmetry
The axis of symmetry for a parabola is given by:
Substitute and :
Axis of Symmetry:
Step 3: Vertex
To find the vertex, substitute into the equation to find :
Vertex:
Step 4: Y-Intercept
The y-intercept occurs when . Substitute into the equation:
Y-Intercept:
Step 5: Graphing
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Key Points:
- Vertex:
- Y-intercept:
- Symmetric Point: Reflect the y-intercept across the axis of symmetry at .
-
Plot the Points: Use to calculate additional points if needed.
-
Shape: The parabola opens upwards because .
Summary of Properties:
- Axis of Symmetry:
- Vertex:
- Y-Intercept:
- Direction: Opens upwards
Would you like a plotted graph for better visualization?
Follow-Up Questions:
- What additional points would you like to calculate for the parabola?
- Do you need assistance with symmetry calculations for graphs?
- Should we explore how changing values affect the parabola's shape and position?
- Would you like a step-by-step guide on completing the square for vertex form?
- How does the vertex relate to the maximum or minimum value of the function?
Tip: Always check symmetry to simplify graphing quadratics!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Graphing Parabolas
Formulas
Axis of symmetry formula: x = -b / 2a
Vertex form: y = ax^2 + bx + c
Y-intercept: c in y = ax^2 + bx + c
Theorems
Properties of Parabolas
Symmetry of Quadratic Functions
Suitable Grade Level
Grades 9-11