find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function

f(x)=x^2-4x-5

F(x) = Y = X^2 - 4X - 5, h = Xv = -b/2a

= 4/2 = 2, K = Yv = 2^2 - 4(2) -5 = -9
V(h,K), V(2,-9). Since a is positive,
the graph opens upward and the vertex
is the min. point on thr graph. To graph the function,select values of X to the left and right of the vertex and
calculate the corresponding value of Y: (0,-5) (1,-8), V(2,-9), (3,-8),
(4,-5).
Line of symmetry:X = 2

a = coefficient of X^2.
h = X-coordinate of vertex.
K = Y- coordinate of vertex.

To find the vertex, line of symmetry, maximum/minimum value, and graph the quadratic function, you can follow these steps:

Step 1: Identify the coefficients of the quadratic function.
The given quadratic function is f(x) = x^2 - 4x - 5. From this, we can see that the coefficient of x^2 is 1, the coefficient of x is -4, and the constant term is -5.

Step 2: Find the vertex.
The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a is the coefficient of x^2 and b is the coefficient of x.
Substituting the values, we get: x = -(-4) / (2*1) = 4/2 = 2.
To find the corresponding y-coordinate, substitute the x-coordinate into the quadratic function: f(2) = (2)^2 - 4(2) - 5 = 4 - 8 - 5 = -9.
Hence, the vertex is (2, -9).

Step 3: Find the line of symmetry.
The line of symmetry is the vertical line that passes through the vertex. In this case, the line of symmetry is x = 2.

Step 4: Determine the maximum/minimum value.
Since the coefficient of the x^2 term is positive, the parabola opens upwards, which means it has a minimum value. The y-coordinate of the vertex represents the minimum value of the quadratic function. In this case, the minimum value is -9.

Step 5: Graph the quadratic function.
To graph the quadratic function, plot the vertex (2, -9) on the graph. Since the line of symmetry is x = 2, you can plot a few more points on either side of the vertex to sketch the parabola symmetrically. Once you have enough points, connect them smoothly to form a smooth curve that represents the parabolic shape of the function.