Question

Write a function for the graph described as a transformation of y=x^2.

Answer 1

we are given

parent function as

$y=x^2$

(1)

vertical stretch of factor 2

so, we can multiply y-value by 2

$y=2x^2$

then a shift right of 3 units

so, we can replace x as x-3

$y=2(x-3)^2$

(2)

a shift left by 2 units

we can replace x as x+2

$y=(x+2)^2$

then a horizontal shrink factor of 1/2

so, we can multiply by 2 to x-value

$y=(2x+2)^2$

then a shift down of 5 units

we can subtract y-value by 5

so, we get

$y=(2x+2)^2-5$

(3)

a shift to the right 1 unit

we can replace x as x-1

$y=(x-1)^2$

stretched vertically by a factor of 1/2

we can multiply y-value by 1/2

$y=\frac{1}{2} (x-1)^2$

then is shifted down 4 units

we can subtract y-value by 4

$y=\frac{1}{2} (x-1)^2-4$

(4)

reflected across the x-axis

we can multiply y-value by -1

$y=-x^2$

tretched vertically by a factor of 3

multiply y-value by 3

$y=-3x^2$

shifted left 7 units

we can replace x as x+7

$y=-3(x+7)^2$