For which value(s) of a does the curve y=x2+ax+2 have a horizontal tangent line at x=1 ? (without using differentiation rules)

Answer 1

y = x² + ax + 2 is an upward opening parabola.

The horizontal tangent is at the vertex.

Use completion of the square to transform into vertex form.

(x + a/2)² + 2 - (a²/4)

a / 2 = -1

a = -2

Answer 2

y = (x + a/2)² + 2 - a²/4;

Horizontal tangent line at vertex. So, - a/2 = 1; a = - 2