Question 1146943
The horizontal line y = k intersects the parabola with equation y = 2(x-3)(x-5) at points A and B. If the length of line segment AB is 6, what is th value of k?
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y = 2(x-3)(x-5) = 2x^2 -16x + 30
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The zeroes are 3 & 5, and the vertex is (4,-2)
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Find the equation of the "similar" parabola with vertex (0,-2)
Its zeroes are -1 & +1.
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y = ax^2 + bx + c
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At (-1,0): 0 = a - b + c
At (1,0): 0 = a + b + c
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b = 0
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At (0,-2): -2 = c
--> y = 2x^2 - 2
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Find y where x = -3 or +3
y = 2*9 - 2 = 16
---> k = 16
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Might be a "better" or shorter way, but k = 16 regardless.