What is the first step in completing the square for the equation $$x^2 + 6x = 5$$ ?

Move the constant term to the other side: $$x^2 + 6x = 5$$ becomes $$x^2 + 6x - 5 = 0$$ .

How do you find the value to complete the square for $$x^2 + 6x$$ ?

Take half of the coefficient of $$x$$ (which is 6), square it (resulting in 9), and add it to both sides of the equation.

What is the completed square form of $$x^2 + 6x - 5 = 0$$ ?

The completed square form is $$(x + 3)^2 - 14 = 0$$ .

What is the solution to the equation $$(x - 3)^2 = 49$$ ?

The solutions are $$x = 10$$ and $$x = -4$$ .

How do you solve the equation $$x^2 + 12x = 5$$ by completing the square?

Rearrange to $$x^2 + 12x - 5 = 0$$ , complete the square to get $$(x + 6)^2 - 41 = 0$$ , then solve for $$x$$ .

What is the significance of the vertex in a quadratic function?

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

What does it mean if the discriminant of a quadratic equation is positive?

If the discriminant (b^2 - 4ac) is positive, the quadratic equation has two distinct real solutions.

What does it mean if the discriminant of a quadratic equation is zero?

If the discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).

What does it mean if the discriminant of a quadratic equation is negative?

If the discriminant is negative, the quadratic equation has no real solutions (the solutions are complex).

How can you verify your solution after completing the square?

You can verify your solution by substituting the values back into the original equation to check if both sides are equal.

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

The coefficients determine the shape, direction, and position of the parabola on the graph.

What is the vertex form of a quadratic equation?

The vertex form is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

Completing the Square Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial, allowing for easier solutions.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the formula to find the new C-term when completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

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