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
11th Grade11thGrade 11 Math
Understand the parabola shape, vertex, axis of symmetry, intercepts, domain, and range that define every quadratic function.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026