Question

use the function y+2=-(x-3)^2 to answer the following.
A) show or explain how you would find the vertex.
B) show or explain how to find the axis of symmetry.
C) show or explain how you would find the x-intercepts.
D) show or explain how you would find the y-intercept.
E) Graph the function.

I know that i first need to convert the function to vertex form y=(x-h)^2+k by subtracting 2 from both sides. which makes it y=-(x-3)^2 -2

Answer 1

@jim_thompson5910

Answer 2

`I know that i first need to convert the function to vertex form y=(x-h)^2+k by subtracting 2 from both sides. which makes it y=-(x-3)^2 -2`

a great start so far

Answer 3

And i know that the vertex is (3,-2) but i dont know how to show work for how i got that answer

Answer 4

there's not much work to show really. You're comparing that equation you got with the template `y = a(x-h)^2 + k`

`(h,k)` is the vertex

Answer 5

so to answer the question i write,
"i first need to convert the function to vertex form y=(x-h)^2+k by subtracting 2 from both sides. which makes it y=-(x-3)^2 -2
we know that (h,k) is the vertex, so the vertex is (3,-2)" ?

Answer 6

I would have "we know that (h,k) is the vertex of y = a(x-h)^2 + k" or something like that

Answer 7

we know that (h,k) is the vertex of y=a(x-h)^2+k so in the case of y=-(x-3)^2-2, the vertex is (3,-2)
better?

Answer 8

yeah that looks good

Answer 9

`B) show or explain how to find the axis of symmetry.`

the axis of symmetry of `y=a(x-h)^2+k` is `x = h`. It is the vertical line through vertex.

Answer 10

so the axis of symmetry for y=-(x-3)^2 -2 is x=3

Answer 11

yes

Answer 12

or -3?

Answer 13

x = 3 since h = 3

Answer 14

x intercepts

Answer 15

To find the x-intercepts, plug in y = 0 and solve for x

Answer 16

wait hold on, x=3 because h=3 ? what?

Answer 17

the vertex in general is (h,k)

in this case, the vertex is (3,-2)

notice how the h and 3 come first in the ordered pairs, so h = 3

Answer 18

in general, the axis of symmetry is x = h

in this problem, the axis of symmetry is x = 3

Answer 19

so i write "the AOS of y=a(x-h)^2+k is x=h. it is the vertical line through the vertex. so the AOS for y=-(x-3)^2-2 is 3, making x=3"

is that what i should have written?

Answer 20

yeah something like that

Answer 21

Ok. Then back to x intercepts. make y=0

Answer 22

then solve for x