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quadratic equation

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There are a graph of y=kx^2-14x+40. It cuts the x-axis at two points A(4,0) and B, and passes through the point C(14,c). Find the area of ABC. THANK U!

最佳解答:

There are a graph of y=kx^2-14x+40. It cuts the x-axis at two points A(4,0) and B, and passes through the point C(14,c). Find the area of ABC. A(4,0) is point on the graph. 0=k(4^2)-14(4)+40 16k-56+40=0 16k-16=0 16k=16 k=1 y=x^2-14x+40 Put y=0 x^2-14x+40=0 (x-4)(x-10)=0 x-4=0 or x-10=0 x=4 or x=10 The coordinates of point B are (10,0). C(14,c) is a point on the graph. c=14^2-14(14)+40 =40 The coordinates of point C are (14,40). The length of the base of △ABC is : AB = 10-4=6 The length of the height of △ABC is 40. The area of △ABC is : 6 x 40 / 2 = 120 unit square.

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