How do you complete the square for the equation $$x^2 - 2x + 7 = 0$$ ?

To complete the square, rewrite it as $$(x - 1)^2 = -6$$ .

What is the value of $$b$$ in the equation $$x^2 + bx + c$$ if you want to complete the square?

The value of $$b$$ is the coefficient of $$x$$ in the quadratic equation.

What do you do with the coefficient of $$x$$ when completing the square?

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

What is the solution to the equation $$9x^2 + 3 = -1$$ ?

The solution is $$\frac{2}{3}i$$ .

What is the significance of the imaginary unit $$i$$ in solutions?

The imaginary unit $$i$$ indicates that the solutions are complex numbers, which occur when the square root of a negative number is involved.

How do you find the value to complete the square for $$x^2 - 12x + ?$$ ?

The value is 36, since $$(-6)^2 = 36$$ .

What is the general form of a quadratic equation?

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What does it mean if a quadratic equation has no real solutions?

It means that the discriminant (b^2 - 4ac) is less than zero, resulting in complex solutions.

What is the discriminant of a quadratic equation?

The discriminant is given by the formula $$D = b^2 - 4ac$$ and determines the nature of the roots of the quadratic equation.

How can you verify if a quadratic equation can be solved by completing the square?

If the equation can be rearranged into the form of a perfect square trinomial, it can be solved by completing the square.

What is the relationship between completing the square and the quadratic formula?

Completing the square is a method that derives the quadratic formula, which provides a direct way to find the roots of any quadratic equation.

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.

Solving Quadratics by Completing the Square FLASHCARD

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, HSA.APR.C.4, HSN.CN.A.1

Standards-aligned

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FLASHCARD QUESTION

Front

What is the process of completing the square?

Back

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

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

Tags

CCSS.HSA.APR.C.4

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Add 14 to both sides of the equation.

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

Back

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

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