How do you solve $$ (x - 7)^2 = 99 $$ using the Square Root Property?

Take the square root of both sides: $$ x - 7 = \text{±} \\sqrt{99} $$ . Then, solve for x: $$ x = 7 \text{±} 3\\sqrt{11} $$ .

What are the solutions to $$ x^2 = 49 $$ ?

The solutions are $$ x = 7 $$ and $$ x = -7 $$ .

How do you solve $$ 2(2x - 4)^2 = 32 $$ ?

First, divide both sides by 2: $$ (2x - 4)^2 = 16 $$ . Then, take the square root: $$ 2x - 4 = \text{±} 4 $$ . Solve for x to get $$ x = 0 $$ and $$ x = 4 $$ .

What is the solution to $$ 3 + 9r^2 = 12 $$ ?

Subtract 3 from both sides: $$ 9r^2 = 9 $$ . Divide by 9: $$ r^2 = 1 $$ . Take the square root: $$ r = 1 $$ and $$ r = -1 $$ .

How do you solve $$ x^2 + 12 = 5 $$ ?

Subtract 12 from both sides: $$ x^2 = -7 $$ . Since the square of a real number cannot be negative, the solutions are $$ x = \text{±} i \\sqrt{7} $$ .

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

It means that the expression under the square root (the discriminant) is negative.

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root: $$ b^2 - 4ac $$ . It determines the nature of the roots.

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 and @@ a eq 0 @@.

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

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

What is the significance of the Square Root Property in solving quadratic equations?

It allows for a straightforward method to find solutions when the equation is in the form of a perfect square.

What is a perfect square trinomial?

A perfect square trinomial is an expression of the form $$ (a + b)^2 = a^2 + 2ab + b^2 $$ or $$ (a - b)^2 = a^2 - 2ab + b^2 $$ .

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

The roots of a quadratic equation correspond to the x-intercepts of its graph, where the parabola intersects the x-axis.

What is the vertex of a parabola?

The vertex is the highest or lowest point of the parabola, depending on its orientation, and can be found using the formula $$ x = -\frac{b}{2a} $$ .

Solving Quadratic Equations using the Square Root Property Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Square Root Property?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

7.

FLASHCARD QUESTION

Front

What is the first step in solving a quadratic equation using the Square Root Property?

Back

Isolate the squared term on one side of the equation.

Tags

CCSS.HSA-REI.B.4B

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