Question

Find the maxima and minima coordinates of the vertext of the parabola of y= x^2-8x+1

Answer 1

This is a parabola, so it can either open upwards and have a min but not a max or open downwards and have a max but not a min. From the sign of the leading term (+1), we know this opens up.

The minimum position of this parabola would be the point of symmetry. To find this, we solve for the zeroes and average those.

The zeroes are found when y = 0. Some quadratic formula later, we get roots of (8 +/- sqrt(60))/2. The average is 4.