Give the vertex and axis of symmetry of the quadratic function.
f(x) = x^2 - 2x - 8
To find the vertex and axis of symmetry of a quadratic function, you can use the formula:
Axis of Symmetry: x = -b/ (2a)
Vertex: (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
For the given quadratic function: f(x) = x^2 - 2x - 8,
we can identify the coefficients as follows: a = 1, b = -2, and c = -8.
To find the axis of symmetry, we will use the formula x = -b/ (2a):
x = -(-2) / (2 * 1) [replace b with -2 and a with 1]
x = 2 / 2
x = 1
The axis of symmetry is x = 1.
To find the vertex, substitute the x-coordinate of the axis of symmetry (1) into the function f(x):
f(1) = (1)^2 - 2(1) - 8
f(1) = 1 - 2 - 8
f(1) = -9
So, the y-coordinate of the vertex is -9. Therefore, the vertex is (1, -9).
In summary:
- Axis of symmetry: x = 1
- Vertex: (1, -9)