What is the axis of symmetry in a quadratic function?

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

How do you check your factored solution?

To check a factored solution, expand the factors back into standard form and verify that it matches the original quadratic equation.

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

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

A binomial is a polynomial with two terms, such as $$x + 3$$ or $$2x - 5$$ .

What is the zero-product property?

The zero-product property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ . This is used to find the roots of factored equations.

What is completing the square?

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form $$(x - p)^2 = q$$ , making it easier to solve for $$x$$ .

What is the standard form of a quadratic equation?

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

How do you factor the quadratic equation $$x^2 - 5x + 6 = 0$$ ?

To factor $$x^2 - 5x + 6 = 0$$ , find two numbers that multiply to 6 and add to -5. The factors are $$(x - 2)(x - 3) = 0$$ , giving roots $$x = 2$$ and $$x = 3$$ .

Solving Quadratics by Factoring 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 does it mean to factor a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What are the roots of a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

How do you determine if a quadratic can be factored?

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7A

7.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

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