Solve All 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 equation?

Back

Factoring a quadratic equation means expressing it as a product of its linear factors, such as (x - p)(x - q) = 0, where p and q are the roots of the equation.

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

How do you find the roots of a quadratic equation?

Back

To find the roots of a quadratic equation, you can set the equation to zero and use factoring, the quadratic formula, or completing the square.

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

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the coefficient of the x² term: if it is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x.