Quadratic Functions

[visual garden]

coyld anyone help pls ? :)

[next flame]

dear lord

ok so

maybe a sketch might be useful

heres a sketch

now

you might need to think back to gcse but

theres actually a nice way to write a quadratic so you can just read out the coordinate of its maximum point

theres also an alevel way tho to find a maximum value

what do you think @visual garden

[visual garden]

differentiation?

[next flame]

could do yep

so if our curve is modelled as that

h + kx - 1/2 x^2

how might we find the turning point

[visual garden]

complete the square?

[next flame]

oh so

those are actually

two different methods

both will work on their own

[visual garden]

oh hahaha

[next flame]

which do you wanna do

both are fine

[visual garden]

ill differentiate

[next flame]

cool

[visual garden]

so would dy/dx be k-x

[next flame]

that looks good yep

and so if our turning point is at

(2,5)

what can we say

[visual garden]

do we input 2 and 5 into the differentiated equation

[next flame]

not both

what do we know about

turning points and differentiated equations

[visual garden]

the differentiated equation = 0 if ur finding a turning point?

[next flame]

yep! so

you can say that

oh and that

its = 0 when its at the turning point right

but we know that

whats x at our turning point

[visual garden]

2 ?

[next flame]

yeah so

when x=2

our differentiated thing should = 0

right?

[visual garden]

ohhh so would k be 2

[next flame]

yep!

so thats part already done

we know its y = h + 2x - 1/2 x^2

now finding h

what do you think

[visual garden]

so do i input 2 as x , 5 as y and k as 2

[next flame]

yep sounds good

[visual garden]

i got 3=h

[next flame]

yeah looks good

[visual garden]

and then for b, are the values of h and k the same

and y=0

[next flame]

yep

[visual garden]

okayyy tysm

life saver 🙏