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A parabola has a maximum value of 4 at x=-1, a y-intercept of 3 , and an x-intercept of 1 .

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Final answer:

The question concerns finding the equation of a parabola with a given maximum value, y-intercept, and x-intercept, using the general form y=ax²+bx+c.

Step-by-step explanation:

The question involves determining the equation of a parabola given certain points and a maximum value. Since the parabola has a maximum value, it will open downwards, indicating the coefficient of the x² term will be negative. The general form of the quadratic equation is y = ax² + bx + c. We know that the y-intercept is 3, which means c = 3. The x-intercept is 1, giving us one point on the graph (1,0). The maximum value of the parabola is 4 at x = -1, so the vertex form of the parabola could be written as y = a(x + 1)² + 4. Using this vertex form, we can plug in the x-intercept to solve for the coefficient a, which would give us the complete parabolic equation.

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