maths question

[hardy rivet]

can someone help me work this out please

anyone?

[hot crown]

I'm still doing gcse so idk if I'm right but this is what I'm thinking:

Quadratic graphs are symmetrical so if the negative x axis has a difference of -6 from the max point (which is where the line of symmetry is) then the positive x axis would be 4 (which is the coordinate of the maximum point) + 6

So the graph intersects positive x at (10, 0)

Quadratic equations:
ax²+bx+c = 0
Oryou can factorise and get:
(x+?)(x+?)
This factorisation will tell us that the x + something = 0 for both and then each value of x will be a coordinate of interception.

The 2 intersection points are -2 and 10
Therefore:
(x+2)(x-10)

Then expand: x² - 8x - 20
f(x) = x² -8x -20

Can someone confirm if this is correct 😅

[hardy rivet]

i feel like what ur saying is correct, however once you complete the square on x^2-8x-20 it does not give you the turning point of (4,24)

[golden compass]

you can't assume the turning point is in the center

i thought the same thing

[golden compass]

i'm thinking

parabola

and

line

but i'm gcse so idek how to do those i just know of them

[burnt briar]

You forgot to add a scalar k f(x)=k(x+2)(x-10)

We know the turning point so substitute and solve for k
Then expand the quadratic

|| f(x)=k(x+2)(x-10) at x=4 y=24 substitute into the equation
We get 24=k(6)(-6)
24=-36k
k=-2/3||

if we have the correct x solutions and x coordinate point of the turning point.All there is left is to scale up or down the y coordinate by stretching parallel to the y direction by some constant

|| f(x)=-2/3 * (x+2)(x-10)
f(x)=2/3x^2-16/3x-40/3||

[hardy rivet]

ahh yess

[tender wigeon]

yeh my method was similar but you got a simultaneous equation w 3 unknowns,
f(x) = ax^2 + bx + c,
f'(x) = 2ax + b, f'(4) = 0,
so 8a + b = 0
a(-2)^2 + b(-2) + c = 0
so 4a - 2b + c= 0
a(4)^2 + b(4) + c = 24
so 16a + 4b + c = 24
eliminate c, then eliminate b and then sub a into them and you get the same answer

[hardy rivet]

thank you so much

[hardy rivet]

thank you very much

[burnt briar]

No problem

[golden compass]

ur a god for year 10

[hardy rivet]

i know right

[hot crown]

Ooh so I wasn't that far off was I?