Question

write the equation in vertex form for a function that has a vertex of (-2, 4) and passes through point (1, -2).

Answer 1

what is 'vertex' form?

Answer 2

vertex is just the y = (x)^2 + ...

Answer 3

we know its off center: y-4 = (x+2)^2 is a good start

Answer 4

we plug in our point to see if we need to adjust the right hand side

Answer 5

-2-4 = (1+2)^2 +C

-6 = 3^2 +C

-6 = 9 + C

-15 = C
.......................
y-4 = (x+2)^2 -15 or:

y = (x+2)^2 -11

Answer 6

for a given parabolic equation we hav,
ax^2+bx+c=y

the co-ordinates of the vertex is: (-b/2a,c-b^2/4a)...
so now put the given points into this...
-b/2a=-2=>b=4a and substituing (1,-2) in the equation we hav, a-2b+c=-2
and also c-4a=4.
thus summarising the relations we got,
b=4a
c-4a=4
-7a+c=-2
solve for a,b nd c ... equations is ready!

Answer 7

..... needs more \(LaTeX\) :)