Question

What are the coordinates of the vertex of the following function? f\x = -x^2-2x+3

(1, 4)
(-1, 4)
(4, -1)
(4, 1)

Answer 1

The vertex of the quadratic function f(x) = -x^2 - 2x + 3 is at the coordinates (-1, 4). This is calculated using the vertex formula for a parabola in standard form. Therefore correct option is B

Step-by-step explanation:

The coordinates of the vertex of the quadratic function can be found using the formula for the vertex form of a parabola. The given quadratic function is f(x) = -x^2 - 2x + 3.

Since the standard form of the quadratic function is ax^2 + bx + c, comparing it to the given function we have a = -1, b = -2, and c = 3.

The vertex can be found at the point (h, k), where h is -b/(2a) and k is f(h).

Let's calculate the x-coordinate (h) of the vertex:

h = -(-2) / (2*(-1))

= -1

Now, let's calculate the y-coordinate (k) by plugging h into f(x):

k = f(-1)

= -(-1)^2 - 2*(-1) + 3

= 4

Therefore, the vertex of the quadratic function is at the coordinates (-1, 4).