The curve y = x2 + 8x − 1 meets the x-axis at the points A and B The point C is (2, 5) Find the area of triangle ABC

Question

the curve curve y = x(to the power of 2) + 8x − 1 meets the x-axis at the points A and B the point c is (2,5) find the area of the triangle ABC

Answer 1

y=x²+8x-1 meets the x-axis (y=0) when

x²+8x=1,

x²+8x+16=1+16=17,

(x+4)²=17,

x+4=±√17,

x=-4±√17, making A=(-4-√17,0), B(-4+√17,0).

If AB is the base then AB=2√17.

Height of ∆ABC is the y-coordinate of C=5.

Area=½(2√17)(5)=5√17=20.62 units² approx.