## Online Course Discussion Forum

### 2021 8 week prep course for AMC 10, hw questions

2021 8 week prep course for AMC 10, hw questions

Hi, i have a question for 4,7, and 9.

Also, is the answer for #10 "6"?

Re: 2021 8 week prep course for AMC 10, hw questions

I just finished #4.  It's a pretty tough question.  Took me a solid 20-25 minutes

Hint 1: Remember that vertices are -b/2a in standard forms of equations (ax^2 + bx + c)

Hint 2: They intersect at one point. What does that tell you about the solution of it?  (Discriminant maybe?)

Re: 2021 8 week prep course for AMC 10, hw questions

By the way these were hints for #4

Re: 2021 8 week prep course for AMC 10, hw questions

Tip for #7: Graph it!

Re: 2021 8 week prep course for AMC 10, hw questions

This is for week 2 assignment, correct? Please always make sure to mention which assignment you are referring to. Also, make sure you let us know what you have tried so far so we can give you better hints.

Here are some hints to get you started:

4: The equation of a parabola with vertex $(h,k)$ looks like $y - k = a(x - h)^2$ for some $a \neq 0$. This $a$ is the leading coefficient of the quadratic.

7: The graphs will intersect at a point $(x_0,y_0)$ iff $(x_0,y_0)$ satisfies BOTH equations. Use this to find the intersection points (in terms of $L$), and then find which values of $L$ make the $y$-coordinate of the point non-negative.

9: Recall $a$ is a root of a polynomial (in $x$) iff $(x-a)$ is a factor.

Re: 2021 8 week prep course for AMC 10, hw questions

Anyone have any hints for #10?

Also, is the answer for question number 7 (3)?

Re: 2021 8 week prep course for AMC 10, hw questions

Try using the given equation and subsitute y^2 for ?, then repeatedly use it, eventually substituting x for y

Re: 2021 8 week prep course for AMC 10, hw questions

I've tried every single way to factor it; can't get a solid final answer.

What I start with:  (tell me if/where I made a mistake)

1/x-1/y=1/x+y  --- how would I isolate one of the variables?

After that I should be able to solve the problem. Thanks, whoever helps me

Re: 2021 8 week prep course for AMC 10, hw questions

Complete the square or use quadratic equation on x in terms of y or vice versa