Question

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

Explanation:

Step1: Identify parent function

Parent function is $y = x^2$, graphed here.

Step2: Determine transformation type

Vertical shift: $y = x^2 + k$ shifts up $k$ units.
Here $k=5$, so shift up 5 units.

Step3: Transform key points

Take parent points:
$(0,0) \to (0, 0+5)=(0,5)$
$(1,1) \to (1, 1+5)=(1,6)$
$(2,4) \to (2, 4+5)=(2,9)$
$(3,9) \to (3, 9+5)=(3,14)$
$(-1,1) \to (-1, 1+5)=(-1,6)$
$(-2,4) \to (-2, 4+5)=(-2,9)$
$(-3,9) \to (-3, 9+5)=(-3,14)$

Step4: Plot transformed points

Connect the new points to form the parabola $y=x^2+5$.

Answer:

The graph of $y = x^2 + 5$ is the parent parabola $y = x^2$ shifted vertically upward by 5 units, with key transformed points $(0,5)$, $(\pm1,6)$, $(\pm2,9)$, $(\pm3,14)$ connected to form the new parabola.