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

The first step is to move the constant $$c$$ to the right side of the equation, resulting in $$x^2 + bx = c$$ .

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

To complete the square, take half of $$b$$ , square it, and add it to both sides of the equation. This value is $$\frac{b}{2}$$ .

What does it mean to factor a quadratic equation?

Factoring a quadratic equation means expressing it as a product of two binomials, such as $$ax^2 + bx + c = (px + q)(rx + s)$$ .

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 solve $$x^2 - 8x - 20 = 0$$ by completing the square?

1. Move -20 to the right: $$x^2 - 8x = 20$$ . 2. Add $$16$$ (which is $$\frac{-8}{2}^2$$ ) to both sides: $$x^2 - 8x + 16 = 36$$ . 3. Factor: $$(x - 4)^2 = 36$$ . 4. Solve: $$x - 4 = \text{±}6$$ , giving $$x = 10$$ or $$x = -2$$ .

What is the solution to the equation $$x^2 + 9x + 9 = 0$$ by completing the square?

1. Move 9 to the right: $$x^2 + 9x = -9$$ . 2. Add $$\frac{9}{2}^2 = \frac{81}{4}$$ to both sides: $$x^2 + 9x + \frac{81}{4} = -9 + \frac{81}{4}$$ . 3. Factor: $$(x + \frac{9}{2})^2 = \frac{45}{4}$$ . 4. Solve: $$x + \frac{9}{2} = \text{±}\frac{3\text{√}5}{2}$$ .

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 first step to solve the equation $$2a^2 + 10a = -12$$ by completing the square?

The first step is to divide both sides by 2 to simplify the equation to $$a^2 + 5a = -6$$ .

What does it mean to write two equations when solving by completing the square?

After rewriting the equation in the form $$(x - p)^2 = q$$ , you take the square root of both sides, leading to two equations: $$x - p = \text{±}\text{√}q$$ .

What is the importance of isolating the variable in solving quadratic equations?

Isolating the variable allows you to simplify the equation and make it easier to solve for the unknown, leading to clearer solutions.

Solving Quadratic Equations by Completing the Square

Flashcard

•

Mathematics

•

6th - 9th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, 6.G.A.1, HSA.APR.C.4

Standards-aligned

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FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

FLASHCARD QUESTION

Front

What does it mean to complete the square?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

What is the formula for the area of a triangle?

Back

Tags

CCSS.6.G.A.1

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

Tags

CCSS.HSA.APR.C.4

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSA-REI.B.4B

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