How do you complete the square for the equation $$x^2 - 6x = 7$$ ?

1. Move 7 to the left: $$x^2 - 6x - 7 = 0$$ . 2. Take half of -6, square it: $$(-3)^2 = 9$$ . 3. Add 9 to both sides: $$x^2 - 6x + 9 = 16$$ . 4. Factor: $$(x - 3)^2 = 16$$ .

What is the solution to the equation $$x^2 - 4x - 5 = 0$$ using completing the square?

1. Move -5: $$x^2 - 4x = 5$$ . 2. Complete the square: $$x^2 - 4x + 4 = 9$$ . 3. Factor: $$(x - 2)^2 = 9$$ . 4. Solve: $$x - 2 = \\pm 3$$ , so $$x = 5, -1$$ .

What does it mean for a quadratic to have complex solutions?

A quadratic has complex solutions when the discriminant (b^2 - 4ac) is less than zero, indicating that the parabola does not intersect the x-axis.

How do you derive the quadratic formula from completing the square?

Starting from the standard form $$ax^2 + bx + c = 0$$ , divide by a, move c/a, complete the square, and solve for x to derive $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

What is the discriminant of a quadratic equation?

The discriminant is the expression $$b^2 - 4ac$$ that determines the nature of the roots of the quadratic equation.

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.

How do you solve $$x^2 + 10x + 21 = 0$$ by completing the square?

1. Move 21: $$x^2 + 10x = -21$$ . 2. Complete the square: $$x^2 + 10x + 25 = 4$$ . 3. Factor: $$(x + 5)^2 = 4$$ . 4. Solve: $$x + 5 = \\pm 2$$ , so $$x = -3, -7$$ .

What is a perfect square trinomial?

A perfect square trinomial is an expression of the form $$(a + b)^2 = a^2 + 2ab + b^2$$ .

What is the relationship between completing the square and graphing a quadratic function?

Completing the square allows you to rewrite the quadratic in vertex form, making it easier to graph by identifying the vertex and axis of symmetry.

How can you check your solution after completing the square?

You can check your solution by substituting the values back into the original equation to see if they satisfy it.

Completing the Square Flashcards

Student preview

15 questions

Show all answers

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

What is the vertex form of a quadratic equation?

Back

5.

FLASHCARD QUESTION

Front

What is the first step in completing the square?

Back

The first step is to move the constant term to the other side of the equation.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Take half of 8 (which is 4) and square it (4^2 = 16). Add 16 to both sides of the equation.

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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