The given quadratic equation is y = (x-5)² - 2.
This equation is in vertex form, which is y = a(x-h)² + k, where (h, k) is the vertex of the parabola.
Comparing the given equation with the vertex form, we can see that h=5 and k=-2.
Therefore, the vertex of the parabola is (5, -2).
Since the coefficient a is positive, the parabola opens upwards.
To find the x-intercepts, we need to set y = 0 and solve for x:
0 = (x-5)² - 2
Adding 2 to both sides, we get:
2 = (x-5)²
Taking the square root of both sides, we get:
±√2 = x-5
Adding 5 to both sides, we get:
x = 5 ± √2
So the x-intercepts are (5+√2, 0) and (5-√2, 0).
To find the y-intercept, we need to set x = 0:
y = (0-5)² - 2 = 23
So the y-intercept is (0, 23).
We can also plot the vertex and intercepts on a coordinate plane to see the shape of the parabola.