Question

the movement of the progress bar may be uneven because questions can be worth more or less (inc\
which of the functions is represented by the graph?\
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\\( f(x) = \frac{1}{2}x^2 + 4 \\)\
\\( f(x) = -\frac{1}{2}x + 4 \\)\
\\( f(x) = -x^2 + 4 \\)\
\\( f(x) = -\frac{1}{2}x^2 + 4 \\)\
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submit \
pass \
dont know answer

Explanation:

Step1: Identify parabola direction

The graph opens downward, so the coefficient of $x^2$ is negative. Eliminate options A (positive coefficient).

Step2: Check vertex y-intercept

The vertex is at (0,4), so the constant term is 4. All remaining options (B, C, D) have +4.

Step3: Analyze coefficient magnitude

Option B is linear (not quadratic, matches graph shape? No, graph is quadratic). Option C: $f(-2)=-(-2)^2+4=0$; option D: $f(-2)=-\frac{1}{2}(-2)^2+4=2$. From the graph, when $x=\pm2$, $y>0$ (not 0), so eliminate C. Thus D is correct.

Answer:

D. $f(x) = -\frac{1}{2}x^2 + 4$