# How does the discriminant affect the graph?

Oct 24, 2014

$a {x}^{2} + b x + c = y$, $D = {b}^{2} - 4 a c$

when a>0 and D > 0, parabola is open towards +ve y-axis (upwards) and intersects the x-axis at two points (Ex: $y = {x}^{2} - 4 x + 3$)

When a>0 and D=0, parabola is open towards +ve y-axis (upwards) and touches x-axis (Ex: $y = {x}^{2} + 4 x + 4$)

When a>0 and D<0, parabola is above x-axis and is open towards +ve y-axis (Ex: $y = {x}^{2} + 2 x + 3$)

When a<0 and D>0, Parabola is open towards -ve y-axis (downwards) and intersects x-axis (Ex: $y = - {x}^{2} + 4 x - 3$)

When a<0 and D=0, Parabola is open towards -ve y-axis (downwards) and touches x-axis (Ex: $y = - {x}^{2} - 4 x - 4$)

when a<0 and D<0, Parabola is open towards -ve y-axis (downwards) and is below x-axis (Ex: $y = - {x}^{2} + 2 x - 3$))

uhh... To make it clear, in the first three cases, the parabola looks like the letter 'U' and in the last three cases, it looks like inverted 'U'.
:D :)