Question

write the equations in standard form of two quadratic functions that have the same vertex but open in different directions.

Answer 1

first write in vertex form
(x-1)^2 + 2
-(x-1)^2 +2

Answer 2

the -1 in the brackets gives the x coordinate of the vertex The negative in front of the brackets in second equation flips the whole graph in the y-direction

Answer 3

so we now expand the eqautions to standard form;
x^2 - 2x + 3 = 0 and
-x^2 +2x +1 = 0

Answer 4

Thank you so much for your help! I completely understand how to do this, except one part: how did you get the constant in the second function in standard form as 1?

Answer 5

-(x-1)^2 + 2 = -(x^2-2x + 1) +2 = -x^2 +2x -1 +2
= -x^2 +2x + 1

Answer 6

'm having difficulty with this website - i cant post a large message more that a few lines so i have to squash it up!

Answer 7

It's no problem really, thank you so much!!