Question

graph the function using a combination of transformations applied to the graph of a basic function.

\\g(x) = 5(x + 3)^2 - 1\\

Explanation:

Identify the base function and transformations

$$
LATEXBLOCK0
$$

Determine key points on the transformed graph

$$
LATEXBLOCK1
$$

Answer:

To graph the function \(g(x) = 5(x + 3)^2 - 1\), apply the following transformations to the basic parabola \(y = x^2\):

1. Shift the graph horizontally to the left by 3 units.
2. Stretch the graph vertically by a factor of 5.
3. Shift the graph vertically down by 1 unit.

The resulting parabola has its vertex at \((-3, -1)\) and passes through the points \((-4, 4)\) and \((-2, 4)\).