Questions: Which graph represents the solution of y ≥ x^2 + 2?

Transcript text: Which graph represents the solution of $y \geq x^{2}+2$ ?

Solution

Step 1: Identify the base parabola

The inequality is $y \geq x^2 + 2$. The corresponding equation is $y = x^2 + 2$. This is a parabola that opens upwards with its vertex at $(0, 2)$.

Step 2: Determine the shaded region

Since the inequality is $y \geq x^2 + 2$, the shaded region should be above the parabola, including the parabola itself (because of the $\geq$ sign).

Step 3: Analyze the given graphs

The first graph shows the region above the parabola $y=x^2+2$ shaded. The second graph shows the region below the parabola $y=x^2+2$ shaded.

The first graph represents the solution of $y \geq x^2 + 2$. $\boxed{\text{First graph}}$

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