Find area of the isosceles triangle formed by the vertex and the x-intercepts of parabola y=x^2-14x-21.
+129847 y = x^2 - 14x - 21
x coordinate of the vertex = 14/2 = 7
y coordinate of the vertex = 7^2 - 14 (7) - 21 = -70
Roots
x^2 - 14x = 21 complete the square on x
x^2 - 14x + 49 = 21 + 49
(x - 7)^2 = 70
x - 7 = ± sqrt 70
x = sqrt (70) + 7
x = -sqrt (70) + 7
Distance between these points = ( sqrt (70) + 7 ) - ( -sqrt (70 + 7) = 2sqrt (70)
Area of triangle = (1/2) (2 sqrt (70) ) ( 70) = 70*sqrt (70) ≈ 585.66
