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# Tutor profile: Patricia S.

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Patricia S.
University research scientist with science, math, coding expertise
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## Questions

### Subject:Pre-Calculus

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Question:

How do I find the x- and y-intercepts of a quadratic function?

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Patricia S.

Consider the generalized function: $$y = ax^2+bx+c$$ In order to find where this function crosses the x- and y-intercepts, let's think about what an intercept is. The x-intercept is the position on the x-axis where the function crosses the x-axis. This means that at this position, the y-value is 0. We can use that to find the x-intercept. So... at x-intercept: y = 0 At y-intercept, x = 0 We'll start with the y-intercept because it is simpler. To find the y-intercept of any equation, plug x = 0 in: $$y = a (0)^2 + b(0) + c = c$$ The y-intercept is c. Correct. Now let's do the x-intercept. To find the x-intercept, plug y = 0 in: $$0 = ax^2 + bx + c$$ We can solve for x using the quadratic formula. This formula gives us the "roots" of the quadratic equation, where the roots are the x-intercept(s). $$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ There could be 0, 1, or 2 x-intercepts of this equation. 0: The function never crosses the x-axis. 2: The function crosses the x-axis in 2 places. 1: The function crosses one time (probably a linear function, or quadratic where a=0).

### Subject:LaTeX

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Question:

Why should I use LaTeX instead of Microsoft Word for writing my lab report?

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Patricia S.


### Subject:Calculus

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Question:

What is the difference between an integral and a sum?

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Patricia S.

An integral can be thought of as a sum across continuous data. Let's revisit the difference between continuous and discrete data. If you have a graph of $f(x)$ vs. $x$, continuous data would be that in which the data is represented by a line, while discrete data is represented by points. One way would be to go outside every hour and take the temperature and put that on a plot. This would give you a set of discrete data: 8 AM: 30 degrees 9 AM: 32 degrees 10 AM: 33 degrees And so on. You have individual measurements that you would plot as points on a plot. Another way would be to use a temperature logger that measures continuously throughout the day so that you know the temperature at every time. This would produce a set of continuous data, or, a smooth curve of data. Let's consider a function $y = f(x)$ from $x = 0$ to $10$. The x-axis of data in a continuous distribution would be represented by: $$0<x<10$$ While data in a discrete distribution from 0 to 10 would be: $$x = 0, 1, 2, ..., 9, 10$$ The y-axes for a continuous distribution would be: $$y = f(x), 0<x<10$$ And for a discrete distribution: $$y = f(x), x = 0,1,2,...,9,10$$ $$y = f(0), f(1),f(2),...,f(9),f(10)$$ You can imagine again that if you were to draw the distribution of $y$ vs $x$, you would use a smooth line for the continuous distribution and a set of points for the discrete distribution. Now if we want to take a total over these two distributions, we get to the integral vs. sum question. An integral calculates the total over a continuous distribution: $$\int_0^{10} f(x)dx$$ While the sum calculates the total over a discrete distribution. $$\sum_{i=0}^{i=10} f(x_i)$$ If you are calculating a sum or integral, the first question you should ask yourself is: Is my data discrete or continuous?

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