Question

Find the x and y intercepts of the quadratic equation f(x)=-x^2+4x-4

Answer 1

X - Intercept
f(x) = -x² + 4x - 4
   0 = -x² + 4x - 4
   x = -(4) +/- √((4)² - 4(-1)(-4))
                         2(-1)
   x = -4 +/- √(16 - 16)
                    -2
   x = -4 +/- √(0)
               -2
   x = -4 +/- 0
              -2
   x = -4 + 0      x = -4 - 0  
            -2                 -2
   x = -4             x = -4
         -2                   -2
   x = 2               x = 2

The solution to the problem is {2, 2}, or {2}. The x - intercept of the problem is (2, 0).

Y - Intercept
f(x) = -x² + 4x - 4
f(x) = -(0)² + 4(0) - 4
f(x) = -(0) + 0 - 4
f(x) = -0 + 0 - 4
f(x) = 0 - 4
f(x) = -4

The y - intercept of the problem is (0, -4).