Determine the x-intercept and y-intercept: y = 3x^2 - 21x + 30

1. To find the y-intercept, set x = 0 in the equation y = 3x^2 - 21x + 30 :
y = 3(0)^2 - 21(0) + 30 = 30
So, the y-intercept is (0, 30).

2. To find the x-intercepts, set y = 0 in the equation 0 = 3x^2 - 21x + 30 and solve for x :
- Factor the quadratic equation:
3x^2 - 21x + 30 = 0
3(x^2 - 7x + 10) = 0
x^2 - 7x + 10 = 0
- Solve the factorized equation:
(x - 2)(x - 5) = 0
- Find the zeros:
x = 2 \text{ or } x = 5
So, the x-intercepts are (2, 0) and (5, 0).

Therefore, the final intercepts are:
x \text{-intercepts: } (2, 0) \text{ and } (5, 0)
y \text{-intercept: } (0, 30)