Find the coordinates of the vertex and the equation of the axis of symmetry of the parabola given by the equation.

y = − 1/7 x^2 + x − 3

and graph it

y = -1/7 x^2 + x - 3

= -1/7 (x^2 - 7x) - 3
now complete the square
y = -1/7 (x^2 -7x + (7/2)^2) - 3 + 1/7 (7/2)^2

y = -1/7 (x - 7/2)^2 - 5/4

Now you can just read off the coordinates of the vertex, no?

graph at

http://www.wolframalpha.com/input/?i=-1%2F7+x^2+%2B+x+-+3

To find the coordinates of the vertex and the equation of the axis of symmetry of a parabola given by the equation, we can use the standard form of a quadratic equation:

y = ax^2 + bx + c

Comparing this with the given equation y = −(1/7)x^2 + x − 3, we have:
a = -1/7
b = 1
c = -3

The x-coordinate of the vertex, denoted as h, can be found using the formula:
h = -b / (2a)

In this case, substitute the values of a and b:
h = -1 / (2 * (-1/7))
h = -1 / (-2/7)
h = 7/2

Now, to find the y-coordinate of the vertex, denoted as k, substitute the value of h back into the equation:
k = a(h^2) + b(h) + c

Substituting the values:
k = -1/7 * (7/2)^2 + 1 * (7/2) - 3
k = -49/28 + 7/2 - 3
k = -49/28 + 98/28 - 84/28
k = -35/28

So, the coordinates of the vertex are (7/2, -35/28).

The equation of the axis of symmetry, denoted as x = h, can be obtained from the x-coordinate of the vertex:
x = 7/2 is the equation of the axis of symmetry.

To graph the parabola, you can follow these steps:
1. Plot the vertex point (7/2, -35/28) on the coordinate plane.
2. Find two additional points on either side of the vertex. To do this, choose x-values that are equidistant from the vertex. For example, you can choose x = 3 and x = 2. Use these x-values to calculate the corresponding y-values using the equation.
3. Connect the three points to form a smooth curve. This curve represents the graph of the parabola.

Make sure to label the axis of symmetry and any other relevant points on the graph.