How many roots does yx2-3x 4 have?

The equation ( y = x^2 - 3x + 4 ) is a quadratic function. To determine the number of roots, we can use the discriminant ( D = b^2 - 4ac ), where ( a = 1 ), ( b = -3 ), and ( c = 4 ). Calculating the discriminant gives ( D = (-3)^2 - 4(1)(4) = 9 - 16 = -7 ). Since the discriminant is negative, the equation has no real roots, indicating that the graph does not intersect the x-axis.