Match the Function y = -1/2x² + 4 to Its Corresponding Graph

One function

$y=-\frac{1}{2}x^2+4$

to the corresponding graph:

To solve for the graph that matches the function $y = -\frac{1}{2}x^2 + 4$, let's analyze the function:

• The function $y = -\frac{1}{2}x^2 + 4$ is a parabola in standard form $y = ax^2 + bx + c$, with $a = -\frac{1}{2}$, $b = 0$, and $c = 4$.
• Because $a = -\frac{1}{2}$ is negative, the parabola opens downwards.
• The vertex of the parabola $y = ax^2 + bx + c$ is at $x = -\frac{b}{2a}$. Here, $b = 0$, so $x = 0$.
• Substituting $x = 0$ back into the equation gives the vertex's y-coordinate: $y = -\frac{1}{2}(0)^2 + 4 = 4$.
• Thus, the vertex is $(0, 4)$.

Now, let's match this to the graphs:

• We are looking for a graph with a vertex at $(0, 4)$ that opens downwards.
• Upon reviewing the graphs in the problem, graph number 1 presents a downward opening parabola with a vertex at the point $(0, 4)$.

Therefore, the graph that corresponds to $y = -\frac{1}{2}x^2 + 4$ is graph 1.

Thus, the solution to the problem is 1.