What value should be added to both sides when completing the square for $$x^2 + 6x = 7$$ ?

The value to be added is $$9$$ , calculated as $$\frac{6}{2}^2$$ .

What is the next step after rewriting $$(x + 2)^2 = 100$$ ?

Take the square root of both sides to get $$x + 2 = \\pm 10$$ .

What is the completed square form of $$x^2 + 8x + 16 = 9 + 16$$ ?

The completed square form is $$(x + 4)^2 = 25$$ .

What is the next line when completing the square for $$x^2 - 4x + 4 = 5 + 4$$ ?

The next line is $$(x - 2)^2 = 9$$ .

What should be added to both sides for the equation $$x^2 - 12x = 21$$ ?

You should add $$36$$ , calculated as $$\frac{-12}{2}^2$$ .

How do you find the vertex of a quadratic function in the form $$y = a(x - h)^2 + k$$ ?

The vertex is the point $$(h, k)$$ .

What is the relationship between the coefficients of a quadratic equation and its graph?

The coefficient $$a$$ determines the direction of the parabola (upward if $$a > 0$$ , downward if $$a

What is the significance of the discriminant in a quadratic equation?

The discriminant $$D = b^2 - 4ac$$ indicates the nature of the roots: if $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

What is the first step in completing the square for the equation $$x^2 + bx = c$$ ?

The first step is to move $$c$$ to the other side of the equation.

How do you derive the value to complete the square from the coefficient $$b$$ ?

Take half of $$b$$ , square it, and add it to both sides of the equation.

What is the completed square form of $$x^2 + 10x + 25 = 0$$ ?

The completed square form is $$(x + 5)^2 = 0$$ .

What does it mean if a quadratic equation can be factored into a perfect square?

It means that the quadratic has a double root, indicating that the vertex of the parabola touches the x-axis.

Completing the Square Practice Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the formula to complete the square for a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the purpose of completing the square in a quadratic equation?

Back

Completing the square allows us to rewrite the quadratic in vertex form, making it easier to analyze its properties such as vertex and axis of symmetry.

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