Question

How does the discriminant affect the graph?

Answer 1

`ax^2+bx+c=y`, `D=b^2-4ac`

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^2-4x+3`)

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

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

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

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

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