Solving & Factoring Quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

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Factoring a quadratic expression involves rewriting it as a product of its linear factors, such as (x - p)(x - q), where p and q are the roots of the equation.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

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

Back

The discriminant, given by b² - 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.

Front

How do you solve a quadratic equation by factoring?

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To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 and x - q = 0.

Front

What is the greatest common factor (GCF)?

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The GCF is the largest factor that divides two or more numbers or expressions without leaving a remainder.

Front

How do you apply the zero product property?

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The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.