Pre-Calc Unit 3 _ Parabolas

Distance Formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

Parabola

the set of all points in a plane that are equidistant froma point, called a focus, and a given line, called a directrix

Standard form of vertical Parabola

y=a(x-h)^2+k

Standard form of a horizontal Parabola

x=a(y-k)^2+h

Focus of a vertical parabola

(h, k + 1/4a)

Axis of Symmetry for "y=" parabola

x=h

Directrix for "y=" parabola

y=k-1/4a

When does a parabola open up?

when "a" is positive

When does the parabola open down?

when a is negative

Vertex of an "x=" parabola

(h,k)

Focus of a horizontal parabola

(h + 1/4a, k)

Axis of symmetry of a "x=" equation

y=k

directrix of a "x=" parabola

x=h-1/4a

When does a parabola open right?

if a is greater than 0

When does a parabola open left?

if a is less than 0