vertex form: 𝑦 = 2(𝑥 − 1)^2 + 3.
a) Use the values of a and q to find the number of x-intercepts.
In vertex form, the equation is in the form y = a(x-q)^2 + p.
Comparing it with the given equation, we can see that a = 2 and q = 1.
To find the number of x-intercepts, we need to look at the value of a.
If a > 0, the parabola opens upwards and does not intersect the x-axis, so there are no x-intercepts.
If a < 0, the parabola opens downwards and does intersect the x-axis, so there will be either one or two x-intercepts.
In this case, a = 2 > 0, so the parabola does not intersect the x-axis, and there are no x-intercepts.