Bridge Math - Quadratic Equations

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 are the solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called the roots of the equation.

Front

How can you find the roots of a quadratic equation?

Back

Roots can be found using factoring, completing the square, or applying the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

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 does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

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 formula x = -b/(2a).

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, located at the coordinates (h, k) where h = -b/(2a) and k is the value of the quadratic function at x = h.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as f(x) = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots.

Front

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

Back

A quadratic opens upwards if the coefficient a > 0 and downwards if a < 0.