Question

graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in section 1.2 and then applying the appropriate transformations.
$y = (x + 3)^2$

Explanation:

Step1: Identify standard parent function

The parent function is $y = x^2$, a parabola with vertex at $(0,0)$, opening upward.

Step2: Determine transformation type

The given function is $y=(x+3)^2$, which is a horizontal shift of the parent function. For $y=(x-h)^2$, $h=-3$, so it shifts left 3 units.

Step3: Locate new vertex

Shift vertex $(0,0)$ left 3 units: new vertex is $(-3, 0)$.

Step4: Match to correct graph

The top graph has vertex at $(-3,0)$, matching the transformed parabola.

Answer:

The correct graph is the top option (the parabola with vertex at $(-3, 0)$ opening upward).