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### Course: Digital SAT Math > Unit 8

Lesson 11: Quadratic graphs: medium# Nonlinear equation graphs — Basic example

Watch Sal work through a basic Nonlinear equation graphs problem.

## Want to join the conversation?

- How to immediately realize which equation belongs to which types of line?(14 votes)
- Notice that if you solve for y in the second equation, you would get a common linear equation of the form y = mx + b, for which you know that the graph must be a straight line. In the second equation, the y variable is squared while the x variable is not, this hints you that the graph would be similar to the one of a quadratic equation (a.k.a a parabola, but flipped since y is squared, not x). The third equation is in the form of the standard circle equation, which makes it easy to guess the graph.

You just have to familiarize yourself with the different types of graphs and equations. And/Or you could solve for y and try to figure out what the plot might look like. :))(23 votes)

- Can someone tell me where on KHAN ACADEMY ONLY where I will find the equations of the circle, like how to plot it and stuff?(5 votes)
- How many licks does it take to get to the center of a lollipop?(6 votes)
- It depends on the lollipop really, it can range from somewhere between 364 to 1000.(2 votes)

- Where can I find more examples of Nonlinear equation graphs?

This section is really troubling me a lot.

Thanks and Regards,

Student(8 votes)- Try searching up "nonlinear equation graphs in the search bar in the top left.(0 votes)

- 'As x increases, y increases at a decreasing rate' and 'As x increases, y decreases at an increasing rate' what does these two statements mean?(3 votes)
- These two statements deal with how the slope of the graph changes over time. You can think of the slope as “rise over run”, or the ratio of how y changes to how x changes. When you have nonlinear equations, the slope isn’t constant as how it would be if you had a straight line. The good thing is that you don’t have to worry much more than that.

If you had a straight line, the statement would be “As x increases, y increases at a constant rate”. If y increases at an increasing rate, the slope (because change in y is the numerator) also increases. If y increases at a decreasing rate, the slope decreases.

Basically, these problems ask you two questions. If y increases as x increases, the slope is positive, and the slope is negative if y decreases. If the slope is getting larger in magnitude (as in y = x^2) the rate is increasing, and if the slope is getting smaller (as in y = 1/x) the rate is decreasing.(6 votes)

- If my graph is upside down, is it still compatible with three equations given? THANKQ in advance.(3 votes)
- so how did u realize that x= 0 like how 3x^2 become zero

I don't get that point ? could you plz repeat(2 votes)- We want to find the y-coordinate of the point where the x-coordinate is 0. To do this, all you have to do is plug in 0 for x in the equation:

y = 3x^2 - 12x + 9

y = 3(0)^2 - 12(0) + 9

y = 9

As you can see, whenever you raise 0 to a power, or multiply or divide it by anything, the answer will still be 0. We can use this as a shortcut: in a polynomial function, because it has terms that are all x raised to a power and multiplied by something, the y-intercept will be equal to the constant term, or the term that is not multiplied by an x. Here, we see that the only term that doesn't have an x is 9, making the answer 9.(2 votes)

- I don't understand the y^2 graph. to me that isn't a possible graph because the y is squared therefore there cannot be any points below the x-axis, in the negative y area. I might be wrong, but i just want a clarification.(2 votes)
- A negative value can also be squared. So the graph can definitely go below the x-axis. Look at how this equation look similar to the quadratic equation. So, it has a similar curved shape (parabola) too. Just that this one is sideways since it is y^2, not x^2.(2 votes)

- If this question did not have the picture of the graphs, what equation will I use?(2 votes)
- Usually these types of questions give you graphs, especially when there are 3 equations.

If it doesn't, it's most likely going to be just two equations, maybe something like:

x^2 + y^2 = 13

y = x - 1(2 votes)

- For the video above is there a way to solve the equations to figure out how many solutions there are instead of looking at the graph?(2 votes)

## Video transcript

- [Instructor] We're told the graph of Y is equal to three X squared minus 12 X plus nine is shown right over here. If the graph crosses the
Y axis at the point 0,K, what is the value of K? Pause this video and see if
you can work through this. All right. So the graph crosses the
Y axis at the point 0. So the X coordinate is zero. Y coordinate is K. So it's at this point, right over here. We would also call that the Y intercept, which is the Y value when the
X coordinate is equal to zero. And to figure that out we just have to look back to the equation. I'll just rewrite it. Y is equal to, and we
see that it's written in standard form, three X squared, minus 12 X plus nine. And so what is Y going to be equal to when X is equal to zero? Well, when X equals zero, that
term's just going to be zero. When X is equal to zero this term's going to be equal to zero. And so Y is going to be equal to nine. And that is choice C and we're done.