Question

solve the equation by graphing the related function.
$x^2 + 3 = 0$
use the graphing tool to graph the parabola.
click to enlarge graph

Explanation:

Step1: Define related function

Rewrite equation as function: $f(x) = x^2 + 3$

Step2: Identify parabola key features

Vertex at $(0, 3)$, opens upward (since coefficient of $x^2$ is positive).

Step3: Analyze x-intercepts

Set $f(x)=0$: $x^2 + 3 = 0 \implies x^2 = -3$. No real solutions, so the parabola never crosses the x-axis.

Answer:

The equation $x^2 + 3 = 0$ has no real solutions. The related parabola $f(x)=x^2+3$ has a vertex at $(0, 3)$, opens upward, and does not intersect the x-axis.