converting the equation from general form to standard form is what you must look to do when dealing with parabolas because standard form gives you just about all the information you need to form a parabola and all you need to do is complete the square just as I have done in the equation above

this week in math we learnt more about parabolas and I tried relating this week to last week and show you how helpful the discriminant truly is.

here we have 3 parabolas that show the different types of discriminant, in the first one the discriminant is greater than zero and intercepts the x-axis twice meaning we have 2 roots

in the next we have the parabola touch the x-axis which means we have only 1 real root

in the last one the parabola doesn’t even touch the x-axis which means we don’t have an intercept and no roots

It’s important to know the discriminant because then you know how many roots your equation will have, for example.

if discriminant < 0 then your equation will have 0 real roots

if discriminant = 0 then your equation will have exactly 1 root

if discriminant > 0 then your equation will have 2 roots

In the equation above I show you where to find the discriminant and I’ve done a question using it, in the question I did the discriminant is less than 0 meaning that it does not have any real roots