Question

solve the equation by graphing the related function.
$x^2 + 2x + 3 = 0$
graph the related function. choose the correct answer below.
a. graph a
b. graph b
c. graph c
d. graph d
help me solve this
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Explanation:

Step1: Define related function

The related function is $y = x^2 + 2x + 3$

Step2: Find vertex of parabola

Use vertex formula $x = -\frac{b}{2a}$. For $ax^2+bx+c$, $a=1, b=2$.
$x = -\frac{2}{2(1)} = -1$
Substitute $x=-1$ into function:
$y = (-1)^2 + 2(-1) + 3 = 1 - 2 + 3 = 2$
Vertex is $(-1, 2)$

Step3: Determine parabola direction

Since $a=1>0$, parabola opens upward.

Step4: Match to graph

Find graph with vertex $(-1,2)$ opening upward.

Answer:

A. <The graph with vertex at (-1, 2) opening upward>