Math Problem Statement
complete the graph of y, equals, left parenthesis, x, minus, 7, right parenthesis, squared, plus, 2y=(x−7) 2 +2.
Solution
To complete the graph of the equation:
Steps to solve:
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Solve for : To express the equation in terms of , divide both sides by 2:
Simplifying:
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Understand the graph's features:
- This is a parabola equation in the form of , where the vertex is at .
- The vertex of this equation is at because the equation is in the form and the constant outside is .
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Identify the direction of the parabola:
- Since the coefficient of is positive (), the parabola opens upwards.
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Plot the vertex:
- The vertex is the point .
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Plot a few other points:
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When , we have:
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When , we have:
So the points and also lie on the parabola.
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Sketch the graph:
- The graph is symmetric about the vertical line (the axis of symmetry).
- The parabola opens upwards, and you can draw it passing through the vertex and the points and .
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Parabolas
Formulas
y = (x - h)^2 + k
y = (x - 7)^2 / 2 + 1
Theorems
Vertex form of a quadratic equation
Properties of parabolas
Suitable Grade Level
Grades 8-10