Factor & Solve Quadratics

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials.

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.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, set the equation to zero, factor the quadratic expression, and then set each factor equal to zero.

Front

What is the Zero Product Property?

Back

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

Front

What is the factored form of the quadratic x^2 - 5x + 6?

Back

The factored form of the quadratic x^2 - 5x + 6 is (x - 2)(x - 3).

Front

How do you determine the number of real roots of a quadratic equation?

Back

The number of real roots can be determined using the discriminant (b^2 - 4ac). If the discriminant is positive, there are two real roots; if it is zero, there is one real root; if negative, there are no real roots.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction of the parabola (opening upwards or downwards). It 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 quadratic formula?

Back

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