Graph Types and Their Standard Equations

Linear

y=mx+b

Rational

y= a/(x−h) +k

Right/Left Parabola

x=a(y−k)² +h

Circle

(x−h)² +(y−k)² =r²

Ellipse

(x−h)²/a² + (y−k)²/b² =1

Hyperbola (horizontal)

(x−h)²/a² − (y−k)²/b² =1

Hyperbola (vertical)

(y−k)²/a² − (x−h)²/b² =1

Vertical Line

x=a

Horizontal Line

y=b

Exponential

y=a⋅b^(x−h) +k

Logarithmic

y=a⋅log_b(x−h)+k

Ray

x(t)=x₁+(x₂−x₁)t, y(t)=y₁+(y₂−y₁)t, where t≥0

Line Segment

x(t)=x₁+(x₂−x₁)t, y(t)=y₁+(y₂−y₁)t, where 0≤t≤1