Question

which graph is defined by the function given below?
y = (x + 3)(x + 3)
a.
b.
c.
d.
a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Step1: Simplify the function

$y=(x+3)(x+3)=(x+3)^2 = x^2 + 6x + 9$

Step2: Find vertex x-coordinate

For $y=ax^2+bx+c$, $x=-\frac{b}{2a}=-\frac{6}{2(1)}=-3$

Step3: Find vertex y-coordinate

Substitute $x=-3$: $y=(-3+3)^2=0$

Step4: Identify vertex location

Vertex at $(-3, 0)$, parabola opens upward (since $a=1>0$)

Answer:

A. Graph A