the only way to find the x-intercepts is to bring it to factored form whether it be from standard form or general form and once you have it in factored form it’s simply like doing an equation between the brackets
The discriminant is related to the x-intercepts in the way that the discriminant will tell you how many intercepts you may have but in the factored form you figure out what the intercepts really are.
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