Properties of Parabolas

These flashcards cover key concepts related to the properties of parabolas as discussed in the lecture.

Parabola

A symmetrical curve formed by the intersection of a cone with a plane parallel to its side.

Vertex Form

An equation of a parabola in the form y = a(x-h)² + k, where (h, k) is the vertex.

Root Form

An equation of a parabola expressed as y = a(x-r₁)(x-r₂), where r₁ and r₂ are the roots.

Maximum value

The highest point of a parabola that opens downwards.

Minimum value

The lowest point of a parabola that opens upwards.

Distinct Root

A root that occurs only once in a quadratic equation.

Identical Roots

The case where the quadratic has a double root, meaning both roots are the same.

Stretch Factor

A constant that affects the width of the parabola; larger factors create narrower parabolas.

No Real Roots

When a parabola does not touch the x-axis, indicating that the quadratic equation has a negative discriminant.

Y-Intercept

The point where the parabola intersects the y-axis.

X-Intercept

The point where a parabola intersects the x-axis, also known as a root.