Math Problem Statement
Which equation is y = –6x2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fourth) squared + thirteen-eighths y = negative 6 (x minus one-fourth) squared + nineteen-eighths y = negative 6 (x minus one-half) squared + seven-halves
Solution
To rewrite the quadratic equation in vertex form, we need to complete the square.
Steps to rewrite in vertex form:
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Start with the given equation:
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Factor out from the first two terms:
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Complete the square:
To complete the square, take half of the coefficient of inside the parentheses (which is ), square it, and add and subtract this value inside the parentheses: So we add and subtract inside the parentheses: -
Rewrite the perfect square:
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Simplify the equation: Now, distribute the :
Thus, the vertex form of the equation is:
The correct choice is:
Would you like further details or have any questions?
Here are five related questions for deeper understanding:
- How do you complete the square in a general quadratic equation?
- What is the vertex of the quadratic equation in vertex form?
- How does the value of affect the graph of a quadratic function in vertex form?
- Can you convert the vertex form back into standard form?
- What are the benefits of expressing a quadratic equation in vertex form?
Tip: The vertex form of a quadratic equation is useful because it easily reveals the vertex of the parabola, making it easier to graph and analyze.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Vertex Form
Completing the Square
Formulas
Standard form of quadratic equation: y = ax^2 + bx + c
Vertex form: y = a(x - h)^2 + k
Completing the square
Theorems
Quadratic Formula
Properties of Parabolas
Suitable Grade Level
Grades 9-12
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