What is the process to complete the square for the expression $$x^2 - 18x + 81$$ ?

1. Take half of the coefficient of $$x$$ (which is -18), square it to get 81. 2. Rewrite the expression as $$(x - 9)^2$$ .

How do you solve the equation $$x^2 + 6x - 3 = 0$$ by completing the square?

1. Move -3 to the other side: $$x^2 + 6x = 3$$ . 2. Complete the square: $$x^2 + 6x + 9 = 3 + 9$$ . 3. Factor: $$(x + 3)^2 = 12$$ . 4. Solve for x: $$x + 3 = \text{±}\frac{2\text{√}3}{1}$$ .

What is the solution to the equation $$x^2 + 12x + 8 = 0$$ ?

1. Move 8 to the other side: $$x^2 + 12x = -8$$ . 2. Complete the square: $$x^2 + 12x + 36 = 28$$ . 3. Factor: $$(x + 6)^2 = 28$$ . 4. Solve for x: $$x + 6 = \text{±}2\text{√}7$$ .

What is the first step in completing the square for the equation $$x^2 + 4x - 16 = 0$$ ?

Move -16 to the other side: $$x^2 + 4x = 16$$ .

What is the vertex form of a quadratic equation?

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

How do you convert a standard quadratic equation to vertex form?

Complete the square on the quadratic equation $$ax^2 + bx + c$$ to express it in the form $$a(x - h)^2 + k$$ .

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

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

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

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

What is the formula for the roots of a quadratic equation?

The roots of a quadratic equation $$ax^2 + bx + c = 0$$ can be found using the quadratic formula: $$x = \frac{-b \text{±} \text{√}(b^2 - 4ac)}{2a}$$ .

What is the importance of completing the square in solving quadratic equations?

Completing the square allows us to rewrite a quadratic equation in a form that makes it easier to solve for the variable, revealing the vertex and the roots.

How can you check if your completed square is correct?

Expand the completed square back to the original quadratic form and verify that it matches the original equation.

CW_HW_Solving Quads by Completing the Square Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

2.

FLASHCARD QUESTION

Front

How do you identify a perfect square trinomial?

Back

A trinomial is a perfect square if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the formula to complete the square?

Back

5.

FLASHCARD QUESTION

Front

What do you do to the b value to correctly complete the square?

Back

Divide the b value by 2 and square the result.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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