Math Problem Statement
Solution
To graph the parabola using the given information:
Given:
- Vertex: (0, 3)
- Point on the parabola:
Step-by-Step Process:
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Identify the form of the parabola's equation: Since you are given the vertex, the vertex form of a quadratic equation is: where is the vertex of the parabola.
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Substitute the vertex coordinates: Given the vertex is (0, 3), substitute and :
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Use the additional point to find the value of : Substitute the coordinates of the point into the equation: Simplify the equation to solve for : Subtract 3 from both sides: Divide by 4:
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Write the final equation: The equation of the parabola is:
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Graph the parabola:
- Plot the vertex at (0, 3).
- Plot the point .
- Since , the parabola opens downward.
- Draw a smooth curve through the points.
You can use the graphing tool provided to plot the vertex and the point, then draw the parabola based on these points.
Would you like a more detailed explanation of any of these steps?
Here are some related questions:
- What is the standard form of a quadratic equation?
- How does the sign of the coefficient affect the direction of the parabola?
- What are other forms of the quadratic equation besides vertex form?
- How do you find the axis of symmetry in a parabola?
- Can you determine the roots of the parabola from the vertex form?
Tip: Always verify the direction of your parabola by checking the sign of the leading coefficient . If is negative, the parabola opens downwards; if positive, it opens upwards.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Graphing Parabolas
Formulas
Vertex form of a quadratic equation: y = a(x - h)^2 + k
Theorems
Vertex form of a parabola
Suitable Grade Level
Grades 9-11