4.5 Completing the Square
Flashcard
•
Mathematics
•
8th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a perfect square trinomial?
Back
A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, typically in the form (a + b)² = a² + 2ab + b².
Tags
CCSS.HSA.APR.C.4
2.
FLASHCARD QUESTION
Front
How do you find the value of c to complete the square for x² + 2x + c?
Back
To find c, take half of the coefficient of x (which is 2), square it (1), and add it to the expression. Thus, c = 1.
Tags
CCSS.HSA-REI.B.4B
3.
FLASHCARD QUESTION
Front
What is the first step in completing the square for the equation x² + 4x + 1 = 0?
Back
The first step is to move the constant term to the other side: x² + 4x = -1.
Tags
CCSS.HSA-REI.B.4B
4.
FLASHCARD QUESTION
Front
What is the formula for completing the square?
Back
The formula is: x² + bx = (x + b/2)² - (b/2)².
Tags
CCSS.HSA-REI.B.4B
5.
FLASHCARD QUESTION
Front
How do you solve x² + 4x + 1 = 0 by completing the square?
Back
1. Move 1 to the other side: x² + 4x = -1. 2. Complete the square: (x + 2)² = 3. 3. Solve for x: x = -2 ± √3.
Tags
CCSS.HSA-REI.B.4B
6.
FLASHCARD QUESTION
Front
What is the solution to (2x - 1)² = 49?
Back
To solve, take the square root of both sides: 2x - 1 = ±7. Thus, x = 4 or x = -3.
Tags
CCSS.HSA-REI.B.4B
7.
FLASHCARD QUESTION
Front
How do you find the missing value c in x² + 26x + c to make it a perfect square?
Back
Take half of 26 (which is 13), square it to get 169. So, c = 169.
Tags
CCSS.HSA-REI.B.4B
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