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

The value of 'c' can be found using the formula $$c = \frac{b^2}{4}$$ .

What is the first step in completing the square for $$x^2 + 8x + c$$ ?

The first step is to take half of the coefficient of $$x$$ (which is 8), square it, and add it to both sides of the equation.

If you have $$x^2 + 4x - 16 = 0$$ , what is the first step to solve it by completing the square?

Rearrange the equation to isolate the constant term: $$x^2 + 4x = 16$$ .

What is the completed square form of $$x^2 + 12x + 8 = 0$$ ?

The completed square form is $$(x + 6)^2 - 28 = 0$$ .

How do you solve $$x^2 + 2x + c$$ to find 'c' for a perfect square?

Set $$c = 1$$ , since $$1 = \frac{2^2}{4}$$ .

What is the formula for finding the vertex of a parabola from the completed square form?

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

What does it mean if a quadratic equation has no real roots when completing the square?

It means that the expression inside the square root becomes negative, indicating that the parabola does not intersect the x-axis.

How do you convert $$x^2 + 8x + 16$$ into completed square form?

It can be written as $$(x + 4)^2$$ .

What is the significance of the discriminant in relation to completing the square?

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots of the quadratic equation.

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

Completing the square is a method that derives the quadratic formula, which is $$x = \frac{-b \text{±} \text{√}(b^2 - 4ac)}{2a}$$ .

How can completing the square help in graphing a quadratic function?

It allows you to find the vertex and axis of symmetry, making it easier to sketch the graph.

What is the general form of a quadratic equation?

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

Completing the Square

Flashcard

•

Mathematics

•

8th - 11th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, HSA.APR.C.4, HSF-IF.C.7A

Standards-aligned

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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, which makes it easier to find the roots.

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

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

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