Quadratic

High School

Definition

From the Latin word "Quadratus" meaning square. In math terms that translates to a degree of 2, think about X squared is \(X^2\). A graph, expression or data that is to a degree of 2 can be defined as quadratic.

Worked examples

\(y = 3x^2 - 5x + 2\)

A quadratic expression in standard form — the highest exponent is 2.

\(f(x) = -x^2 + 4x\)

This quadratic function graphs as a parabola opening downward because the \(x^2\) coefficient is negative.

\(x^2 + 6x + 9 = (x + 3)^2\)

A quadratic expression factored into a perfect square — still degree 2.

Common mistakes

\(2x + 5\) is quadratic → \(2x + 5\) is linear; \(2x^2 + 5\) is quadratic Quadratic means the highest power is 2, not 1.
\(x^3 - x^2 + 1\) is quadratic because it has an \(x^2\) term → \(x^3 - x^2 + 1\) is cubic (degree 3) The degree is determined by the highest power present, not just any squared term.
All parabolas open upward → Parabolas open upward if \(a > 0\), downward if \(a < 0\) in \(ax^2 + bx + c\) The sign of the leading coefficient controls the parabola's direction.

Where you'll use it next

You'll solve quadratic equations using factoring, completing the square, and the quadratic formula; graph parabolas in coordinate geometry; and model projectile motion and optimization problems in algebra, precalculus, physics, and calculus.

Found in 1 StudyPug lesson

Characteristics of quadratic functions

Grade 11 Math

Three properties that are universal to all quadratic functions: 1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior); 2) The domain of a quadratic function is all real numbers; and 3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.

11th Grade11th