Answer:
the vertex is at (4, -14)
Explanation:
Review "quadratic equations." These have three terms, and the highest power of x is x^2. We need to identify the coefficients of the x^2, x and x^0 terms to get info needed to identify the axis of symmetry.
Given f(x) = x^2 - 8x + 2, we see that these coefficients are 1, -8 and 2.
b
The formula for the axis of symmetry is x = - ------
2a
which here is x = -(-8)/[2*1], or x = 8/2 or x = 4: the axis of symmetry.
To find the y-coordinate of the vertex, evaluate the function at x = 4:
f(4) = 4^2 - 8(4) + 2 = 16 - 32 + 2, or f(4) = -14.
Thus, the vertex is at (4, -14). The graph is that of a parabola that opens up, and the parabola is symmetric about the vertical line x = 4.