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# drawing cubic graphs watch

1. last minute question before c1 tomorrow!
when drawing cubics, how do you know where to draw the vertex if you haven't found it out? e.g., i have the cubic x^3 + 2x^2 - 5x - 6
ive found out the factors, so it crosses the x axis at 2, -3 and -1
and i know how to draw the general shape of the cubic graph, but i always draw the minimum/maximum points wrong, as they have to be on a certain side of the y axis and i'm not sure how you're supposed to know where they are? any help? thanks
2. Set and solve it to find the turning points (if any) in the usual way.

Since is a cubic, then will require that you solve a quadratic.
3. (Original post by atsruser)
Set and solve it to find the turning points (if any) in the usual way.

Since is a cubic, then will require that you solve a quadratic.
when you say f'(x) do you mean the derivative?
4. (Original post by georgiaaaxo)
when you say f'(x) do you mean the derivative?
Yes.
5. (Original post by georgiaaaxo)
last minute question before c1 tomorrow!
when drawing cubics, how do you know where to draw the vertex if you haven't found it out? e.g., i have the cubic x^3 + 2x^2 - 5x - 6
ive found out the factors, so it crosses the x axis at 2, -3 and -1
and i know how to draw the general shape of the cubic graph, but i always draw the minimum/maximum points wrong, as they have to be on a certain side of the y axis and i'm not sure how you're supposed to know where they are? any help? thanks
Since the coefficient of x^3 is positive, you know that when x is big and negative, then the cubic is big and negative; and when x is big and positive, the cubic is big and positive.

So start with your pencil down below the the x axis and draw a rough cubic curve upwards till you cross the x-axis at -3; draw up to a peak somewhere between -3 and -1, then come down to cross the axis again at x=-1; then down till there's a trough (minimum) somewhere between -1 and 2, then come upwards to cross the axis at x = -1 again; then keep going upwards to indicate the general shape of the curve.

You can differentiate to get the exact turning points if the question requires you to mark them

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