What is the first step in solving the equation $$(x-3)^2 - 16 = 0$$ ?

The first step is to add $$16$$ to both sides, resulting in $$(x-3)^2 = 16$$ .

What is the result of taking the square root of $$(x-3)^2 = 16$$ ?

The result is $$x - 3 = \text{±}4$$ .

What are the two solutions for $$x - 3 = \text{±}4$$ ?

The two solutions are $$x = 7$$ and $$x = -1$$ .

What does it mean if a quadratic equation has imaginary solutions?

Imaginary solutions occur when the squared term results in a negative number after isolating it, indicating no real x-intercepts.

How do you determine if the solutions of a quadratic equation are real or imaginary?

You determine this by checking if the value under the square root (the discriminant) is positive (real solutions) or negative (imaginary solutions).

What is the discriminant in a quadratic equation?

The discriminant is given by $$b^2 - 4ac$$ and helps determine the nature of the roots of the quadratic equation.

What is the formula for finding the roots of a quadratic equation?

The roots can be found using the quadratic formula: $$x = \frac{{-b \text{±} \text{√}(b^2 - 4ac)}}{{2a}}$$ .

What does the term 'x-intercept' refer to in the context of quadratic equations?

The x-intercept refers to the points where the graph of the quadratic equation crosses the x-axis, which correspond to the solutions of the equation.

What is the vertex of a quadratic function?

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on its orientation.

How can you check your solutions for a quadratic equation?

You can check your solutions by substituting them back into the original equation to see if they satisfy it.

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

The roots of a quadratic equation correspond to the points where the graph intersects the x-axis, indicating the values of $$x$$ for which the equation equals zero.

5.8 Solving Quadratic Equations Using Square Roots Flashcard

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to solve a quadratic equation using square roots?

Back

Solving a quadratic equation using square roots involves isolating the squared term and then taking the square root of both sides to find the variable's values.

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What do you do after isolating the squared term in a quadratic equation?

Back

After isolating the squared term, take the square root of both sides to solve for the variable.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

7.

FLASHCARD QUESTION

Front

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

Back

The solutions, also called roots or zeros, represent the x-intercepts of the quadratic function on a graph.

Tags

CCSS.HSF-IF.C.7A

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