𝑦 = 2(𝑥 − 1)^2 + 3.
a) Use the values of a and q to find the number of x-intercepts.
To find the x-intercepts, we need to set y equal to zero and solve for x. So, let's set y = 0:
0 = 2(x - 1)^2 + 3
Next, we isolate the perfect square term by subtracting 3 from both sides:
-2 = 2(x - 1)^2
Now, let's isolate the perfect square term further by dividing both sides by 2:
-1 = (x - 1)^2
Taking the square root of both sides:
±√(-1) = x - 1
Since we cannot take the square root of a negative number in the real number system, there are no x-intercepts for this equation.
Therefore, the number of x-intercepts is 0.