How do you solve $$x^2 = 16$$ using the square root method?

Taking the square root of both sides gives $$x = \\pm 4$$ .

How do you solve $$(x + 5)^2 - 20 = 0$$ ?

Rearranging gives $$(x + 5)^2 = 20$$ , then taking the square root results in $$x = -5 \\pm \\sqrt{20}$$ .

What are the roots of the equation $$x^2 + 6x - 4 = 36$$ ?

Rearranging gives $$x^2 + 6x - 40 = 0$$ , which factors to $$(x - 4)(x + 10) = 0$$ , so the roots are $$x = 4$$ and $$x = -10$$ .

What are the factors of $$x^2 + 2x - 3 = 0$$ ?

The factors are $$(x - 1)(x + 3)$$ , with solutions $$x = 1$$ and $$x = -3$$ .

How do you solve $$x^2 + 4x + 1 = 0$$ by completing the square?

Rewriting gives $$(x + 2)^2 = 3$$ , leading to $$x = -2 \\pm \\sqrt{3}$$ .

What is the discriminant in a quadratic equation?

The discriminant is given by $$D = b^2 - 4ac$$ and determines the nature of the roots: if D > 0, two real roots; D = 0, one real root; D

What does it mean if a quadratic equation has complex roots?

Complex roots occur when the discriminant is negative, indicating that the solutions involve imaginary numbers.

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.

How can you graph a quadratic equation?

To graph a quadratic equation, find the vertex, axis of symmetry, and intercepts, then plot points to form a parabola.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line given by $$x = -\frac{b}{2a}$$ , which divides the parabola into two mirror-image halves.

What is the significance of the leading coefficient in a quadratic equation?

The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upwards; if a

Solving Quadratic Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, completing the square, using the quadratic formula, and graphing.

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What does completing the square involve?

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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