Quadratics

https://drive.google.com/file/d/1bQN00btpKQRzwsZ60C7OjnEVBiYbdAtZ/view?usp=sharing

For 9a I understand how b=-180a but after that the coordinates (90,30) are substituted into the equation of h. I don’t understand where the y coordinate 30 comes from. Please can someone explain this to me

Reply 1

mqb2766

I get access denied from your google drive. It would probably be best just to post an image of the question/your working here (click on the camera icon in the reply toolbar)

Reply 2

taqiyah

Original post by mqb2766

I get access denied from your google drive. It would probably be best just to post an image of the question/your working here (click on the camera icon in the reply toolbar)

Reply 3

mqb2766

Original post by taqiyah

No idea, whoever did the working should have subbed the point (120,27) which gives the same value for a. They seem to have done this at the very bottom of the page.

(edited 11 months ago)

Reply 4

mqb2766

Original post by taqiyah

Been mulling this over and there are a few ways to go, and cant see a "trivial" way to get that the the maximum occurs at 90,30. The only, a bit connvoluted, reasoning was that by symmetry (60,27) is also a point and therefore the maximum must be 3 + 24*9/8 as the 9 and 8 reflect the squared x distances of the points from the maximum. However, its not an approach Id do.

About the simplest way to solve the problem would be to note that x=90 is a point of symmetry so you can reflect the (0,3) to (180,3) and hence write the quadratic as
h = a*x*(x-180) + 3
Then sub (120,27) to get a and expand. Or using similar reasoning
h = a(x-60)(x-120) + 27
Not that different from the way theyve done it but precalculus.