Question

For the given equation y = (x - 1)² – 3, what is the coordinate of the vertex?

a) (1, -3)
b) (-1, -3)
c) (1, 3)
d) (-1, 3)

Answer 1

The coordinate of the vertex is (1, -3).

Step-by-step explanation:

The equation y = (x - 1)² - 3 represents a quadratic function in vertex form. To find the vertex of the parabola, we can use the formula (h, k), where h = -b/2a and k = f(h).

For the given equation, a = 1, b = -2, and c = -3. Substituting these values into the formulas, we get h = -(-2)/(2*1) = 1 and k = f(1) = (1 - 1)² - 3 = -3.

Therefore, the coordinate of the vertex is (1, -3). Hence, the correct answer is option a) (1, -3).