Han Zhi Yuan's answer to Troubled's Secondary 2 Maths Singapore question.
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The quadratic curve -x^2 + px + q can be expressed as -(x-2)(x-k), where the coordinates of A is (k,0) and the coordinates of B is (2,0).
The average of k and 2 is equal to -1 as the line of symmetry is x = -1.
=> (k+2)/2 = -1
=> k + 2 = -2
=> k = -4
So point A = (-4,0).
Using -(x-2)(x-k), we now have -(x-2)(x+4) = -x^2 - 2x + 8.
=> p = -2, q = 8.
When x = 0, y = -(0)^2 - 2(0) + 8 = 8.
=> Point C = (0,8).
The average of k and 2 is equal to -1 as the line of symmetry is x = -1.
=> (k+2)/2 = -1
=> k + 2 = -2
=> k = -4
So point A = (-4,0).
Using -(x-2)(x-k), we now have -(x-2)(x+4) = -x^2 - 2x + 8.
=> p = -2, q = 8.
When x = 0, y = -(0)^2 - 2(0) + 8 = 8.
=> Point C = (0,8).
Date Posted:
3 years ago
Maximum point of the graph is when x = -1.
=> y = -(-1)^2 - 2(-1) + 8 = (-1) + 2 + 8 = 9.
Coordinate of maximum point = (-1,9)
=> y = -(-1)^2 - 2(-1) + 8 = (-1) + 2 + 8 = 9.
Coordinate of maximum point = (-1,9)
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