How do you factor the expression $$2x^2 + 2x - 12$$ ?

First, factor out the common factor: $$2(x^2 + x - 6)$$ . Then, factor the quadratic: $$2(x - 2)(x + 3)$$ .

What is the factored form of $$x^2 - 7x - 18$$ ?

The factored form is $$(x + 2)(x - 9)$$ .

How do you determine the roots of a quadratic equation?

The roots of a quadratic equation can be found using the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

What does it mean for a quadratic to be 'completely factored'?

A quadratic is completely factored when it is expressed as a product of linear factors, with no further factoring possible.

What is the relationship between the coefficients and the roots 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 $$\frac{c}{a}$$ .

How can you verify if your factored form is correct?

You can verify the factored form by expanding it back to the original quadratic equation.

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

The leading coefficient (the coefficient of $$x^2$$ ) determines the direction in which the parabola opens: if it is positive, the parabola opens upwards; if negative, it opens downwards.

What is the importance of the quadratic formula?

The quadratic formula provides a method to find the roots of any quadratic equation, regardless of whether it can be factored easily.

Flashcard: Writing Quadratic Equations and 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 is the standard form of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

How do you find the axis of symmetry of a parabola?

Back

5.

FLASHCARD QUESTION

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. It can be found using the axis of symmetry.

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

Back

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