need help with writing a quadratic function in vertex form

[wind garden]

I dont the steps to do this but i tried guessing using the vertex form

(h,k)

so since the quadratic function is formatted like this: a (x - h)^2 + k

I tried writing (x + 3)^2 + 5

but the y-intercept is 0,14 when i put it on desmos

so if anyone can help me, i'd really appreciate it 🙏

[viscid shard]

you still need to find a

[wind garden]

idk how

[viscid shard]

y = a(x + 3)^2 + 5

[wind garden]

yeh

[viscid shard]

replace y and x with the given point (0, -14)

and solve for a

[wind garden]

wdym

slope?

[red gyro]

replace the y and x in y = a(x+3)^2+5

with the points in (0,-14)

[wind garden]

wait..

[red gyro]

to find a

[wind garden]

ohhhh

okok i see it

alr hold up

uhh

what do i do here

my working is this
y = a( x + 3)^2 + 5
-14 = a (0 +3) ^2 + 5
-14 = a (3)^2 + 5
-14 = a (9) + 5
-19 = a (9)
a = -2.1111111

?

im assuming it's a fraction but idk how to turn someone help pls

[viscid shard]

well that's it

[red gyro]

-19/9(x+3)^2+5

x+3 mb

[wind garden]

waht

[viscid shard]

you've found the function

[wind garden]

the decimal is complicated

is there any way to turn into fraction?

[red gyro]

write the fraction then

[wind garden]

howwwwww

[red gyro]

yk how u did -19/9 to get the 2.11111111 decimal

[wind garden]

mhm

[red gyro]

-19/9 is the fraction

[wind garden]

oh

ohhh ok

alr tysm @viscid shard @red gyro

.solved