What is the process of completing the square in a quadratic expression?
Complete the Square (Vertex Form)

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Mathematics
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9th - 12th Grade
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Hard
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1.
FLASHCARD QUESTION
Front
Back
Completing the square involves rewriting a quadratic expression in the form of (x - p)² + q, where (p, q) represents the vertex of the parabola.
2.
FLASHCARD QUESTION
Front
What is the vertex form of a quadratic function?
Back
The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
3.
FLASHCARD QUESTION
Front
How do you find the vertex of a parabola given in vertex form?
Back
The vertex can be directly identified as the point (h, k) from the vertex form f(x) = a(x - h)² + k.
4.
FLASHCARD QUESTION
Front
What is the significance of the vertex in a parabola?
Back
The vertex represents the highest or lowest point of the parabola, depending on the direction it opens (upward or downward).
5.
FLASHCARD QUESTION
Front
How do you convert a standard form quadratic equation to vertex form?
Back
To convert, complete the square on the quadratic expression and rewrite it in the form f(x) = a(x - h)² + k.
6.
FLASHCARD QUESTION
Front
What is the first step in completing the square for the expression x² + bx?
Back
The first step is to take half of the coefficient b, square it, and add it to both sides of the equation.
7.
FLASHCARD QUESTION
Front
Given the quadratic expression x² + 6x + 5, what is the completed square form?
Back
The completed square form is (x + 3)² - 4.
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