Question

Write the equation of the quadratic function with roots -2 and 4 and a vertex at (1, 9).

Answer 1

the vertex form of a quadratic is
a(x - h)^2 + k where the vertex is at (h,k)

Answer 2

so in your case we have
f(x) = a(x - 1)^2 + 9

Answer 3

now you need to find the value of a which you can do using the given roots

Answer 4

so what is a?

Answer 5

a is a number to be found

Answer 6

the roots are -2 and 4 so points of intersection on x-axis are (-2,0) and (4,0)
So plugging these values into the above equation and solving for a will give you the final equation

Answer 7

I'm really not good at this. but i think i'm kinda getting it? could you just show me please?

Answer 8

ok f(x) = 0 when a - -2 so
0 = a(-2-1)^2 + 9
0 = 9a + 9
-9a = 9
a = -1

so we;ve found a

Answer 9

so the answer is
f(x) = -1(x - 1)^2 + 9?

Answer 10

yes

Answer 11

thanks so much. i will fan and medal you. :)

Answer 12

they might want it in standard form though
just expand and simplify

Answer 13

yw ty

Answer 14

they haven't asked for that so leaving in in the above form should be ok

Answer 15

yep, that should be fine. thanks again.