Quadratic and Exponential Transformations

$$f\left(x\right)\ =\ a\left(x-h\right)^2\ +k$$

$$f\left(x\right)=\ ab^{\left(x-c\right)}\ +d$$

$$f\left(x\right)\ =\ ax^2\ +bx\ +c$$

$$\left(y-y_1\right)\ =\ m\left(x-x_1\right)$$

-a, reflection

a>1, stretch

0<a<1, compress

-a, reflection

a<1, stretch

a>1, compress

-a, reflection

$$\frac{1}{a}$$ , compress

a>1, stretch

a<1, reflection

-h, shift right

+h, shift left

-h, shift left

+h, shift right

-h, shift down

+h, shift up

-h, shift up

+h, shift down

-k, shift right

+k, shift left

-k, shift left

+k, shift right

-k, shift down

+k, shift up

-k, shift up

+k, shift down

y-intercept

-a, reflection

a>1, stretch

0<a<1, compress

y-intercept

-a, reflection

a<1, stretch

a>1, compress

range

-a, reflection

a<1, compress

domain

a>1, stretch

a<1, reflection

a

b

c

d

-c, shift right

+c, shift left

-c, shift left

+c, shift right

-c, shift down

+c, shift up

-c, shift up

+c, shift down

-d, range

-d, shift right

+d, shift left

range

-d, shift left

+d, shift right

asymptote

-d, shift down

+d, shift up

asymptote

-d, shift up

+d, shift down

shift to the right 3, shift down 7

shift to the left 3, shift down 7

reflects, shift to the left 3, shift down 7

shift to the right 3, shift up 7

shift to the right 5, shift up 3, y-intercept is (0,2)

shift to the left 5, shift up 3, y-intercept is (2,0)

shift to the right 3, shift up 5, y-intercept is (2,0)

shift to the right 2, shift down 5, y-intercept is (0,3)