Question

1. a quadratic function has been vertically compressed by a factor of \\(\frac{1}{4}\\), shifted 1 unit left, and shifted 6 units down. what is its equation?

a. \\(f(x)=\frac{1}{4}(x - 1)^2 - 6\\)
b. \\(f(x)=\frac{1}{4}(x + 1)^2 + 6\\)
c. \\(f(x)=\frac{1}{4}(x + 1)^2 - 6\\)
d. \\(f(x)=4(x + 1)^2 - 6\\)

Explanation:

Step1: Start with parent quadratic

The parent quadratic function is $f(x)=x^2$.

Step2: Apply vertical compression

Vertically compress by $\frac{1}{4}$: multiply by $\frac{1}{4}$, so $f(x)=\frac{1}{4}x^2$.

Step3: Shift 1 unit left

Shift left 1 unit: replace $x$ with $x+1$, so $f(x)=\frac{1}{4}(x+1)^2$.

Step4: Shift 6 units down

Shift down 6 units: subtract 6, so $f(x)=\frac{1}{4}(x+1)^2 - 6$.

Answer:

c. $f(x) = \frac{1}{4}(x+1)^2 - 6$