Do Parabolas and Other Non-Linear Graphs Have Slope?

In summary, the slope of a linear equation can be easily seen as a ratio of change in y-coordinates to change in x-coordinates. However, when the x^2 term in a function is non-zero, the slope changes and can be determined at a specific x-value using the derivative of the function. This slope is that of a tangent line to the function at that point and can vary depending on the function.
  • #1
DS2C
So the slope is of course a ratio of the change in y-coordinates to the change in x-coordinates. This is easy to see with a linear equation.
I just came across a cool math simulator ( https://phet.colorado.edu/sims/equation-grapher/equation-grapher_en.html), and I left the first value (ax^2) alone and messed with the other two, which acted as a normal linear equation because the x^2 value was 0.
But when the x^2 term is a non-zero value, and you change the values of b, the graph gets weird and starts tilting. Is this still the slope changing? Does every graph of every power have slope? I'm having a hard time picturing the slope of a parabola.
 
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  • #2
You can determine the slope at a specific x-value. This is possible for every polynomial and for many other functions as well. It is called the derivative of the function. The derivative of ax2+bx+c is 2ax+b. As you can see, it depends on x. As an example, the slope is zero at x=-b/(2a). At this point the parabola has its minimum or maximum.
 
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  • #3
Ah ok that makes more sense. Thank you.
 
  • #4
What mfb didn't mention is that the slope is that of a tangent line to function at that point. Thus varies point to point depending on the functionl
 
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1. What is the definition of slope for a parabola or other non-linear graph?

The slope of a parabola or other non-linear graph is the change in the y-coordinate divided by the change in the x-coordinate at any given point on the curve. This is represented by the derivative of the function that defines the graph.

2. How do you find the slope of a parabola or other non-linear graph?

To find the slope of a parabola or other non-linear graph, you can use the derivative function, which is a mathematical formula that calculates the slope of a curve at any given point. Alternatively, you can choose two points on the curve and calculate the slope using the rise over run method.

3. Can the slope of a parabola or other non-linear graph be positive or negative?

Yes, the slope of a parabola or other non-linear graph can be positive or negative. The sign of the slope depends on the direction of the curve at any given point. If the curve is increasing, the slope will be positive, and if the curve is decreasing, the slope will be negative.

4. Is the slope of a parabola or other non-linear graph constant?

No, the slope of a parabola or other non-linear graph is not constant. It changes at each point on the curve and is represented by the derivative function. This is because the rate of change of a non-linear graph is not constant and can vary at different points on the curve.

5. How does the slope of a parabola or other non-linear graph affect the shape of the curve?

The slope of a parabola or other non-linear graph affects the shape of the curve by determining its direction at any given point. A positive slope will result in an upward curve, while a negative slope will result in a downward curve. The magnitude of the slope also affects the steepness of the curve at that point.

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