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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 2: Passport to advanced mathematics- Solving quadratic equations — Basic example
- Solving quadratic equations — Harder example
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems — Harder example
- Manipulating quadratic and exponential expressions — Basic example
- Manipulating quadratic and exponential expressions — Harder example
- Radicals and rational exponents — Basic example
- Radicals and rational exponents — Harder example
- Radical and rational equations — Basic example
- Radical and rational equations — Harder example
- Operations with rational expressions — Basic example
- Operations with rational expressions — Harder example
- Operations with polynomials — Basic example
- Operations with polynomials — Harder example
- Polynomial factors and graphs — Basic example
- Polynomial factors and graphs — Harder example
- Nonlinear equation graphs — Basic example
- Nonlinear equation graphs — Harder example
- Linear and quadratic systems — Basic example
- Linear and quadratic systems — Harder example
- Structure in expressions — Basic example
- Structure in expressions — Harder example
- Isolating quantities — Basic example
- Isolating quantities — Harder example
- Function notation — Basic example
- Function notation — Harder example

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# 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?(15 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. :))(21 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?(6 votes)
- Did this in 3 seconds(7 votes)
- Where can I find more examples of Nonlinear equation graphs?

This section is really troubling me a lot.

Thanks and Regards,

Student(6 votes)- Try searching up "nonlinear equation graphs in the search bar in the top left.(1 vote)

- Where can I find lessons for this on Khan Academy (Geometry, Trig, Algebra, etc.)? I typed in "nonlinear equation graphs", but I'm not sure if my results are exactly what I'm looking for or not. I'd like to be able to study this a little bit more outside of the SAT section.(3 votes)
- Top left on Khan Academy homepage. Subjects - Math by subject is on the left side of the drop down menu.(1 vote)

- '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?(2 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.(3 votes)

- If my graph is upside down, is it still compatible with three equations given? THANKQ in advance.(2 votes)
- how do we know the equation with x squared and y squared was the circle(2 votes)
- Well, equations containing x squared and y squared and their coefficient is one are circle equations.(1 vote)

- In the x, y-plane, the point (3,6) lies on the graph of the function f(x)=3x^2-bx+12. What is the value of b?

Correct Answer: 11

can someone please give me a clear answer explanation for this question(1 vote) - 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?(1 vote)

## 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.