The graph of y=x^2-3x+6 has how many intercepts?
(the term x^2 means x squared)
Y = x^2 - 3x + 6.
B^2 = (-3) = 9.
4*A*C = 4*1*6 = 24.
B^2 - 4AC = 9 - 24 = -15 = The value
under the radical.
Since the value under the radical is negative, there are 2 imaginary solutions. Therefore, the graph does not touch or cross the x-axis. So there
are no x-intercepts.
When x = zero, Y = 6. Therefore, the Y-
intercept = 6: (0,6).
NOTE: B^2 = (-3)^2 = 9.
To determine the number of intercepts of the graph of a quadratic equation, we need to consider the discriminant of the equation, which is the expression under the square root in the quadratic formula.
Given the quadratic equation y = x^2 - 3x + 6, we can find the discriminant by using the formula D = b^2 - 4ac. Here, a = 1, b = -3, and c = 6.
Substituting the values into the formula, we have:
D = (-3)^2 - 4(1)(6)
D = 9 - 24
D = -15
If the discriminant is negative, as in this case, the quadratic equation has no real solutions. This means there are no x-intercepts in the graph.
Therefore, the graph of y = x^2 - 3x + 6 has no intercepts on the x-axis.