Which of the following describes the graph of y = -x^2 + 3x + 10?

Answer:

The graph has zeroes at x=-2 and x=5 and it opens downward.

explaination:

To analyze the quadratic function y = -x^2 + 3x + 10, we first find the x-intercepts (zeroes) by setting y to 0. This leads us to the equation 0 = -x^2 + 3x + 10, which simplifies to x^2 - 3x - 10 = 0. Factoring gives us (x - 5)(x + 2) = 0, resulting in zeroes at x = -2 and x = 5. Next, we determine the vertex of the parabola using the formula x = -b/(2a), where a = -1 and b = 3. This gives us x = 3/2. Substituting this back into the function yields the y-coordinate of the vertex as 47/4. Since the coefficient of x^2 is negative, the parabola opens downward. Therefore, the correct description of the graph is that it has zeroes at x = -2 and x = 5 and opens downward.

Topic: Quadratic Functions and Graphs

Tags: quadratic functions graphing parabolas x-intercepts

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Which of the following describes the graph of y = -x^2 + 3x + 10?

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