Question

How did we transform from the parent function? g(x) = -1/5(x - 1)² + 7

Answer 1

Answer:

Horizontal shift to the right

Vertical compression

Reflection across the x axis

Vertical shift up

Step-by-step explanation:

Given that the parent function was $g(x)=x^2$

we notice the following transformations:

a) a horizontal shift to the right in 1 (one) unit rendering: $g(x)=(x-1)^2$

b) a vertical compression by multiplying our function by a number smaller than 1 ( $\frac{1}{5}$ ), rendering: $g(x)=\frac{1}{5} (x-1)^2$

c) a reflection across the x-axis by flipping the sign of the function and rendering: $g(x)=-\frac{1}{5} (x-1)^2$

d) a vertical shift of 7 units up thus giving finally: $g(x)=-\frac{1}{5} (x-1)^2+7$