How many x-intercepts are on the graph of y = 3(x − 2)^2 + 4?
To find the x-intercepts, we need to find the values of x when y is equal to zero. Thus, we set the equation equal to zero:
0 = 3(x - 2)^2 + 4
Subtracting 4 from both sides:
-4 = 3(x - 2)^2
Dividing both sides by 3:
-4/3 = (x - 2)^2
Taking the square root of both sides:
±√(-4/3) = x - 2
Since the square root of a negative number does not yield a real value, there are no x-intercepts on the graph of y = 3(x − 2)^2 + 4.