Final answer:
The function y=3x^2+4x-2 has a horizontal tangent at the point (-2/3, -14/3), which corresponds to option d. after calculating the y-coordinate using the function.
Step-by-step explanation:
The function given is y = 3x^2 + 4x - 2. To find where the function has a horizontal tangent, we look for points where the derivative of the function is equal to zero. The derivative of y with respect to x is dy/dx = 6x + 4. Setting the derivative to zero gives us:
0 = 6x + 4
x = -4/6
x = -2/3
Substituting x = -2/3 into the original function to find the y-coordinate:
y = 3(-2/3) ^2 + 4(-2/3) - 2
y = 3(4/9) - 8/3 - 2
y = 4/3 - 8/3 - 2
y = -12/3 + 4/3 - 6/3
y = -14/3
Thus, the function has a horizontal tangent at the point (-2/3, -14/3), matching option d. with the correct y-value filled in.