Question

Create two additional quadratic functions, g(x) and h(x).

The function g(x) will open the same direction as f(x), have the same vertex, but will be narrower.
The function h(x) will open in the opposite direction as f(x), have the same vertex, but will be wider than f(x).

Write your functions below and explain in complete sentences why those functions will meet the requirements in the question.

Answer 1

was my previous equation

Answer 2

@phi

Answer 3

your question asks for the same vertex
I think it would be easier to use the vertex form of the equation
f(x) = a( x - h)^2 + k (where (h,k) is the vertex)

all parabolas with the same vertex of 11,27 (if I remember it correctly) will have the equation
f(x) = a(x - 11)^2 + 27

notice that all you can change is the "a"

Answer 4

So I can take my old equation and just change the a lol?

Answer 5

would those two work?

Answer 6

the bigger "a" is the skinner the parabola is
the smaller "a" is (but the same sign), the wider the parabola
here is a graph

Answer 7

your h(x) is wider, and has the same vertex, but it opens up the same way as f(x)
they want
h(x) will open in the opposite direction as f(x)

as you can see on the graph, f(x) zooms up.
to get h(x) to zoom down, what sign should "a" have ?

Answer 8

positive I believe?

Answer 9

nevermind, negative

Answer 10

@phi

Answer 11

yes. though people don't bother to write -1 in front. they just write the minus sign
h(x) = -(x-11)^2 + 27

(it means the same thing as h(x) = -1(x-11)^2 + 27)

Answer 12

Alright sweet, only a couple more questions :D

Answer 13

Here they are