a line

a hyperbola

a parabola

a cubic

ax + by = c

y = a(x - h)² + k

y = ax² + bx + c

y = mx + b

y value of the vertex

Axis of Symmetry

Direction (facing up or down)

x-intercept

(5, -4)

(-5, -4)

(-15, -4)

(15, -4)

x=4

x=-4

x=1/2

x=3

(3,4)

(-3,4)

(3, -4)

(-3,-4)

multiply the x² by a fraction

multiply the x² by a decimal

multiply the x² by a negative number

multiply the x² by a number greater than 1

f(x) = (x - 2)² - 1

f(x) = (x + 2)² - 1

f(x) = -(x + 2)² - 1

f(x) = -(x - 2)² - 1

$y=-\left(x-1\right)^2+4$

$y=\left(x-1\right)^2+4$

$y=-\left(x-4\right)^2+1$

$y=\left(x-4\right)^2+1$

$h\left(x\right)=\ \left(x+1\right)^2-4$

$h\left(x\right)=-\left(x+1\right)^2-4$

$h\left(x\right)=\left(x+4\right)^2-1$

$h\left(x\right)=-\left(x+4\right)^2+1$