Axis of symmetry is a line passing through the vertex which divides the curge into two parts such tha each part looks the same.
For [tex]y= x^{2} +3x-4[/tex], the 'x' part is squared and the coefficient of [tex]x^{2}[/tex] is positive. Hence, the curve will be a parabola facing up which means that the axis of symmetry will be a vertical line. i.e. x = m.
Investigating, f(-1) =[tex]= (-1)^{2} +3(-1)-4=1-3-4=-6[/tex]
f(-1.5) = [tex]= (-1.5)^{2} +3(-1.5)-4=2.25-4.5-4=-6.25[/tex]
f(-2) = [tex]= (-2)^{2} +3(-2)-4=4-6-4=-6[/tex]
From these, the curve has a vertex at point (-1.5, -6)
Therefore the axis of symmetry is line x = -1.5 (i.e. the third option)
