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Determine the a-value for the equation, y=a(x+2)(x-6), for the quadratic that intersects the x-axis at the points (-2,0) and (6,0) and passes through (7,27).

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Final answer:

By substituting the coordinates of the point (7,27) into the quadratic equation y=a(x+2)(x-6), we determine that the a-value is 3.

Step-by-step explanation:

To determine the a-value for the equation y=a(x+2)(x-6), we need to use the point through which the quadratic passes, which is (7,27). Since the quadratic intersects the x-axis at the points (-2,0) and (6,0), we know that the equation correctly represents these points for any value of a. Now, substituting the x and y values from the point (7,27) into the equation gives us 27=a(7+2)(7-6). This simplifies to 27=9a, and solving for a gives us a=3. Therefore, the a-value is 3.

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