What are the characteristics of the parabola: f(x) = x^2 – 8x + 7?

The equation of the parabola given is : f(x) = x^2 – 8x +
7

f(x) = x^2 – 8x +
7

=> x^2 - 8x + 16 +
9

=> (x - 4)^2 - 9

The
standard form of the parabola y = a*(x - h)^2 + k can be used to determine all its
characteristics.

Here, a is positive, indicating that the
parabola opens upwards.

The vertex is at (h, k). For the
equation given it is (4, -9)

The the axis of symmetry is x
= 4

The graph does not intersect the
x-axis.

The y-intercept of the parabola is (0,
7).

The x-intercepts can be determined by equating (x -
4)^2 - 9 = 0 and solving for x.

This gives (1, 0) and (7,
0)

The domain of the parabola is all the values that x can
take for real values of y. Here it is R.

The range of the
parabola is all the values y can take for x lying in the domain. Here it is [-9 ,
inf.]