How do you factor the expression $$12x^2 + 8x - 4$$ ?

The factored form is $$4(3x - 1)(x + 1)$$ .

What is the factored form of the quadratic function $$f(x) = x^2 - 9x + 14$$ ?

The factored form is $$f(x) = (x - 2)(x - 7)$$ .

Solve the quadratic equation $$3x^2 - 12 = 0$$ .

The solutions are $$x = -2$$ and $$x = 2$$ .

What is the factored form of $$f(x) = x^2 - 4x - 45$$ ?

The factored form is $$f(x) = (x + 5)(x - 9)$$ .

How do you find the zeros of the function $$f(x) = 2x^2 + 11x + 15$$ using factoring?

The factored form is $$f(x) = (2x + 5)(x + 3)$$ .

What is the quadratic formula?

The quadratic formula is $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ , used to find the solutions of a quadratic equation.

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

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

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

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

What is the vertex form of a quadratic function?

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

How do you determine if a quadratic opens upwards or downwards?

A quadratic opens upwards if the leading coefficient $$a > 0$$ and downwards if $$a

What is the process of completing the square?

Completing the square is a method used to convert a quadratic equation into vertex form by adding and subtracting the square of half the coefficient of $$x$$ .

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

The sum of the roots is equal to $$-\frac{b}{a}$$ and the product of the roots is equal to $$\frac{c}{a}$$ , according to Vieta's formulas.

Review Factoring & Solving Quadratics Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define factoring in algebra.

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

2.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What are the zeros of a function?

Back

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