Question

graph the equation shown below by transforming the given graph of the parent function.
$y = (x + 4)^2 - 5$

Explanation:

Step1: Identify parent function

Parent function is $y = x^2$ (vertex at (0,0)).

Step2: Apply horizontal shift

$y=(x+4)^2$ shifts parent left by 4 units (vertex to (-4,0)).

Step3: Apply vertical shift

$y=(x+4)^2 -5$ shifts down by 5 units (vertex to (-4,-5)).

Step4: Transform key points

For parent points: (0,0)→(-4,-5); (1,1)→(-3,-4); (-1,1)→(-5,-4); (2,4)→(-2,-1); (-2,4)→(-6,-1).

Answer:

Plot the transformed points (-4,-5), (-3,-4), (-5,-4), (-2,-1), (-6,-1) and draw the parabola opening upward with vertex at (-4,-5).