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# Drawing quadratic graphs Watch

1. I've realised understanding roots is rather important to maths AS level, as your knowledge of it is needed to answer some questions. I understand why if then there are two different roots. But what I don't understand is why if then there are two equal roots- as it goes through the x-axis at only one point. :/ Please help me understand as I cannot move on without knowing.
2. (Original post by MathMeister)
I've realised understanding roots is rather important to maths AS level, as your knowledge of it is needed to answer some questions. I understand why if then there are two different roots. But what I don't understand is why if then there are two equal roots- as it goes through the x-axis at only one point. :/ Please help me understand as I cannot move on without knowing.
They are called repeated roots. It's nothing to worry about and there's really nothing here that you're not understanding. It's just convenient to put it that way so that every quadratic equation has two roots, every cubic equation has three roots and so on.

This post may raise more questions than it answers but I'll leave it at that for now.
3. (Original post by MathMeister)
I've realised understanding roots is rather important to maths AS level, as your knowledge of it is needed to answer some questions. I understand why if then there are two different roots. But what I don't understand is why if then there are two equal roots- as it goes through the x-axis at only one point. :/ Please help me understand as I cannot move on without knowing.
There are still two roots, they're just 'repeated'. Consider that

Where you have

If , when you take the square root, you get nothing. Recall that you usually add and subtract the root of the discriminant. Adding or subtracting 0 doesn't change anything, thus you only get one value for , and hence you have a 'repeated root'. Equivalently, the only reason you get two different roots (for other quadratic equations) is because you subtract and add the root of the discriminant.

(Not sure if I'm right—you'd be best to ask your teacher, this is merely what I've understood from perusing Core 1.)
4. I still don't understand. Let's say there's only 1 x-intercept and it seems like there must only be 1 root. But somehow there's 2. Please please explain. I'm rather quick at understanding maths, I've tried to work it out and it would do me the world of good if you could please explain, or if somebody could. Plz
5. (Original post by MathMeister)
I still don't understand. Let's say there's only 1 x-intercept and it seems like there must only be 1 root. But somehow there's 2. Please please explain. I'm rather quick at understanding maths, I've tried to work it out and it would do me the world of good if you could please explain, or if somebody could. Plz
From what I've hearkened to, you get two different values for because you add and subtract the root of the discriminant. What happens if the discriminant is equal to 0? You will add and subtract 0, so the 'two' values you have are the same: but, nonetheless, you still have two values. I.e., the two different values for , graphically, are on the same point: so it looks like you have 1 root only.

If this is still confusing, you should ask your teacher. (Again, not sure if what I posted is correct. )
6. (Original post by MathMeister)
I still don't understand. Let's say there's only 1 x-intercept and it seems like there must only be 1 root. But somehow there's 2. Please please explain. I'm rather quick at understanding maths, I've tried to work it out and it would do me the world of good if you could please explain, or if somebody could. Plz
If there is only 1 x-intercept then there is only 1 root. Likewise if there is only 1 root then there is only 1 x-intercept.
7. I (think i) COMPLETELY UNDERSTAND WOOOOP DA WOOP. and , when equated to zero get . So it's not too incomprehensible to understand why the quadratic has 2 equal roots, as the root applies to both is this right?
8. (Original post by MathMeister)
I (think i) COMPLETELY UNDERSTAND WOOOOP DA WOOP. and , when equated to zero get . So it's not too incomprehensible to understand why the quadratic has 2 equal roots, as the root applies to both is this right?
Every quadratic with a double root can be factorised into the form (x-a)(x-a), so you can view a double root as a number which makes both brackets 0 (where as a normal root would only make one of them 0).
9. Exactly, I hope
10. Who knows what appropriate values for to draw a quadratic function. I understand they should be above or below the roots by a certain amount, but I'm not sure by how much. One example is draw the graphs with the following equations, choosing appropriate values for and . Who knows what, or how to work out the appropriate x values to evaluate.
11. (Original post by MathMeister)
Who knows what appropriate values for to draw a quadratic function. I understand they should be above or below the roots by a certain amount, but I'm not sure by how much. One example is draw the graphs with the following equations, choosing appropriate values for and . Who knows what, or how to work out the appropriate x values to evaluate.
It is normally enough to plot the x intercepts, the y intercepts, and the minimum (or maximum).
12. The c1 book says otherwise.
13. (Original post by MathMeister)
The c1 book says otherwise.
When I did A levels that was all the wa sneeded, it may be different depending on exam board and what the question is. If the question says sketch then you certainly don't need anything else.

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