Question 702280
<br><font face="Tahoma">The equation {{{y=x^2}}} is a quadratic equation.<br>

We can NOT readily find the slope (or rate of change) of this function like we can with a linear equation simply using Algebra.<br>

In fact, there are an infinite amount of slopes at an infinite amount of points for this function.<br>

These slopes are based on the slope of the tangent line to the curve at any given point.<br>

And to find the slope of that tangent line at any given point, we would need to use Calculus.<br>

We would need to calculate the derivative of this function to do so.<br>

The derivative of {{{x^2}}} is simply {{{2x}}}<br>

So at any give point x, the slope of the curve at that point is 2x.<br>

For example, at the point (5,25)<br>

the slope of the tangent line to the curve<br>

is {{{2*5}}} or 10.<br>

But at the point (0,0)<br>

the slope of the tangent line to the curve<br>

is {{{0*5}}} or 0, because the tangent line to the curve at (0,0) is horizontal.<br>

Short answer:<br>

The slope of the tangent line at any point on the curve {{{y=x^2}}}<br>

is given by {{{2x}}}<br>

which is known as the derivative of y wth respect to x.<br>

I hope this helps!  Keep practicing!  :)<br>

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