Complete the Square (Vertex Form)
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the vertex form of a quadratic equation?
Back
The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
2.
FLASHCARD QUESTION
Front
How do you find the vertex from the vertex form?
Back
In the vertex form y = a(x - h)² + k, the vertex is the point (h, k).
3.
FLASHCARD QUESTION
Front
What does completing the square mean in the context of quadratic equations?
Back
Completing the square involves rewriting a quadratic equation in the form y = a(x - h)² + k to easily identify the vertex and graph the parabola.
4.
FLASHCARD QUESTION
Front
Given the equation y = 3(x + 5)² - 4, what is the vertex?
Back
The vertex is (-5, -4).
5.
FLASHCARD QUESTION
Front
Convert the quadratic equation y = x² + 10x + 23 to vertex form.
Back
The vertex form is y = (x + 5)² - 2.
6.
FLASHCARD QUESTION
Front
What is the process to complete the square for the equation f(x) = x² + 6x + 12?
Back
1. Take half of the coefficient of x (which is 6), square it (9), and add/subtract it: f(x) = (x² + 6x + 9) + 12 - 9 = (x + 3)² + 3.
7.
FLASHCARD QUESTION
Front
What is the vertex of the parabola given by y = 2(x - 3)² + 4?
Back
The vertex is (3, 4).
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