given a quadratic function y=a(x-h)^2+k.if its graph is a parabola with the line of symmetry at x=2 and passes through the points (3,7) and (4,11)
a)what is the value of h?
b)find two equations each relating a and k
c)hence solve for a and k,and write down the corresponding quadratic function.
簡單maths
2007-10-16 6:15 am
回答 (1)
2007-10-16 6:28 am
✔ 最佳答案
a) h = 2b) Substitute (3,7) into the equation of the graph,
7 = a(3 - 2)2 + k
a + k = 7 ... (1)
Substitute (4,11) into the equation of the graph,
11 = a(4 - 2)2 + k
4a + k = 11 ... (2)
c) (2) - (1): 3a = 4
a = 4/3
Substitute a=4/3 into (1),
k = 7 - 4/3 = 17/3
So the corresponding quadratic function is y = (4/3) (x - 2)2 + 17/3
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