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You are right in thinking that positive and negative determine up or down, but that's only true for linear functions, for example:
y = x --> Increases (Goes Up)
y = - x --> Decreases (Goes Down)
However, there are certain functions who's shape is determined by the power of x. In these cases, the negative and positive effects how the graph "Opens". For example:
y = (x^2) --> Parabola (Opens Up)
y = - (x^2) --> Parabola (Opens Down)
Note: A parabola looks like a "U" shape. This is due to the x squared, and not the sign. However, notice it will open up due to the positive. The negative will flip our "U" upside down, and so it will open downward instead.
Hope this helps!!
y = x --> Increases (Goes Up)
y = - x --> Decreases (Goes Down)
However, there are certain functions who's shape is determined by the power of x. In these cases, the negative and positive effects how the graph "Opens". For example:
y = (x^2) --> Parabola (Opens Up)
y = - (x^2) --> Parabola (Opens Down)
Note: A parabola looks like a "U" shape. This is due to the x squared, and not the sign. However, notice it will open up due to the positive. The negative will flip our "U" upside down, and so it will open downward instead.
Hope this helps!!
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It sounds like you might be in an algebra or pre-calculus class, so this answer may not be appropriate, but...
As long as the function is nice enough, the derivative tells you where it increases (goes upwards), decreases (goes downwards), or is flat. Essentially, you would find the derivative f '(x), and then see where it is positive, negative, or zero, respectively.
As long as the function is nice enough, the derivative tells you where it increases (goes upwards), decreases (goes downwards), or is flat. Essentially, you would find the derivative f '(x), and then see where it is positive, negative, or zero, respectively.
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Change of the function which is determined by the derivative will show you if the function is decreasing or increasing. f'(x) = negative , the function is decreasing, f(x) = positive , the function is increasing, f'(x)=0 the function is at the turning point.
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graph it
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Depends on the coefficient or the "a" value and the power.
Remember that the equation of a parabola is y=ax^2+bx+c
If the coefficient is positive and an even power such as y=5x^2 you know that the graph opens upward. This is true of all positive coefficients and even powers. It could be y=5x^20 or y=10x^1000 it is going to open upward.
If the coefficient is negative and an even power such as y= -8x^2 you know that the graph opens downward. This is true of all negative coefficients and even powers. It could be y= -8x^20 or y= -11x^1000 it is going to open downward.
Remember that the equation of a parabola is y=ax^2+bx+c
If the coefficient is positive and an even power such as y=5x^2 you know that the graph opens upward. This is true of all positive coefficients and even powers. It could be y=5x^20 or y=10x^1000 it is going to open upward.
If the coefficient is negative and an even power such as y= -8x^2 you know that the graph opens downward. This is true of all negative coefficients and even powers. It could be y= -8x^20 or y= -11x^1000 it is going to open downward.