## Online Course Discussion Forum

### 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"?

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?)

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.

Anyone have any hints for #10?

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

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

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