How do you isolate $$x$$ in the equation $$x^2 = a$$ ?

To isolate $$x$$ , take the square root of both sides: $$x = \text{±}\sqrt{a}$$ .

How do you solve $$x^2 + 5 = -55$$ ?

First, isolate $$x^2$$ : $$x^2 = -55 - 5 = -60$$ . Then, take the square root: $$x = \text{±}\text{√}(-60) = \text{±}2i\text{√}15$$ .

How do you solve $$2x^2 = -16$$ ?

Divide both sides by 2: $$x^2 = -8$$ . Then take the square root: $$x = \text{±}2i\text{√}2$$ .

What is the relationship between square roots and exponents?

The square root of a number can be expressed as an exponent: $$\text{√}a = a^{1/2}$$ .

What does it mean to have complex solutions?

Complex solutions occur when the discriminant of a quadratic equation is negative, resulting in solutions that include imaginary numbers.

How do you solve $$x^2 - 2x^2 = 76$$ ?

Combine like terms: $$-x^2 = 76$$ , then multiply by -1: $$x^2 = -76$$ . Take the square root: $$x = \text{±}2i\text{√}19$$ .

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, given by $$b^2 - 4ac$$ , which determines the nature of the roots.

How do you express a quadratic equation in standard form?

A quadratic equation is in standard form when it is written as $$ax^2 + bx + c = 0$$ .

What is the significance of the vertex in a quadratic function?

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

How do you check your solutions after solving a quadratic equation?

Substitute the solutions back into the original equation to verify that both sides are equal.

Solving by Square Roots

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSA-REI.B.4B, 8.EE.A.2, HSN.CN.A.1

Standards-aligned

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FLASHCARD QUESTION

Front

What is the square root of a negative number?

Back

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

What is the principle of completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

What does it mean to simplify a square root?

Back

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

FLASHCARD QUESTION

Front

What is an imaginary unit?

Back

Tags

CCSS.HSN.CN.A.1

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