Carlos graphs the equations y is equal to negative 1 half x squared plus 4 and y is equal to negative 1 half x squared minus 2 x plus 2 and generates the graph. Which conclusion is supported by the graph?

Set the two expressions for y equal: −½x² + 4 = −½x² − 2x + 2. The −½x² terms cancel, leaving 4 = −2x + 2, so x = −1. The graphs intersect at only this one x-value, so the equation has one real solution: choice C.

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