Question

askew, jordan alg2a 2.1 and 2.2 test. describe the transformations of the parent function (f(x)=x^{2}) represented by (g(x)=2(x + 1)^{2}-8).

Explanation:

Step1: Analyze horizontal shift

For a function of the form $y = a(x - h)^2+k$, the value of $h$ determines the horizontal shift. In $g(x)=2(x + 1)^2-8$, we have $h=- 1$. So, there is a horizontal shift of 1 unit to the left.

Step2: Analyze vertical stretch

The coefficient $a$ in $y = a(x - h)^2+k$ determines the vertical stretch or compression. Here $a = 2$, so the parent - function $f(x)=x^2$ is vertically stretched by a factor of 2.

Step3: Analyze vertical shift

The value of $k$ in $y = a(x - h)^2+k$ determines the vertical shift. Since $k=-8$, there is a vertical shift of 8 units down.

Answer:

The function $g(x)=2(x + 1)^2-8$ is a transformation of the parent function $f(x)=x^2$ that includes a horizontal shift 1 unit to the left, a vertical stretch by a factor of 2, and a vertical shift 8 units down.