Quadratic functions 😍

[pine ferry]

#11 is reflected over the x axis because the coefficient of the x^2 term is negative

that's not true for #12

the domain is the set of values that you can plug into the function and get a valid output, and for these two functions it's easy to see that you can plug in any number and get a valid input so the domain is all reals

[pine ferry]

also, because its x^2 coefficient is negative, that means it's opening downward and so it doesn't have a minimum

for #11 you need to say that it has a maximum

[hard abyss]

the domain for all of our functions (as of right now unless a word problem) is xeR

[hard abyss]

well yea, but thats true for the equation

the question is asking which is NOT true

[pine ferry]

oh yeah

[hard abyss]

im confused on the reflections because they both seem to be reflecting along an “x=something” line, but one has “graph reflects in x axis” as true, but one doesn’t

does that make sense?

(inserted the wrong picture sorry) 12 is blue 11 is green

[pine ferry]

axis of symmetry is a completely different concept to reflections

axis of symmetry is a line which the graph can be reflected across without changing

for parabolas, that will always be the vertical line passing through the vertex

[hard abyss]

i do know that

x=whatever the x coordinate of the vertex

so what are reflection axis? we weren’t taught that 😭

[pine ferry]

compare the graphs to the standard x^2 graph. if they're opening in the same direction as that graph, which would be up, then it's not reflected over the x axis

you can see that the green graph, however, is opening in the opposite direction to the x^2 graph so it had to have been reflected over the x axis

you can imagine taking the x^2 graph and then modifying it until you reach the function in question

[hard abyss]

so blue (12) is NOT reflected in the x-axis, but green (11) is. if i were to look at something how can i tell if it’s reflected or not? what do you mean by comparing it to the x^2 graph?

normally i wouldn’t care this much but i’m locking in to keep my math average what it is currently

[pine ferry]

transformations are relative to the base graph. in this case the base graph is y=x^2
you can tell if the graph is reflected over the x axis based on whether it's opening up or opening down. if its vertex is at the base of the parabola, it's opening up, and if the vertex is at the peak of the parabola, it's opening down

[hard abyss]

so all of the extra numbers in y = a(x-p)^2 + q are just moving around the base quadratic of y = x^2? so since green is opening down, it’s automatically reflected across the x-axis? if that’s the case are all downward-opening parabolas reflected across the x-axis? we only just started this and our teacher hasn’t covered reflections or transformations or base graphs or any of those terms lol. i know what you mean by them now but this info is very reluctant to adhere to my brain

[pine ferry]

yes, yes, and yes

that's all correct

[hard abyss]

okay. that makes a lot of sense. i really wish i knew about this server last year when i was getting cooked in linear equations… thanks 🥲