Please help me check if this is correct

[unreal summit]

7c has its ends going up, meaning the x^2 coefficient is positive, it cannot be -ve

[thorn hedge]

no because its -x^2

-x^2 has an n shape

while x^2 has a u shape

[thorn hedge]

(upside down bucket)

so yk how to find the equation of quadratics with 3 points

so we know where they cross the x-axis( the solutions to the quadratic)

which is

(-48,0) and (32,0)

so x = -48 and x = 32

when we have a quadratic in the form ax^2 + bx + c

we can factorise it

into

$\alpha(x + \beta)(x + \gamma)$

[sand grove]

curry supplier

[thorn hedge]

please work

YAY

[thorn hedge]

ok so from this

the solutions to $\alpha(x + \beta)(x + \gamma) = 0$ are $x = -\beta$, $x = -\gamma$

[sand grove]

curry supplier

[thorn hedge]

and we know whta the solutions to 7c is

x = -48 and x = 32

so we know that

$-\beta = -48$, $-\gamma = 32$

[sand grove]

curry supplier

[thorn hedge]

btw im just using beta and gamma for variables you could use anything but im using this for clarity

[thorn hedge]

and we want to know what $\beta$ is and what $\gamma$ is so that we can add them in our equation

[sand grove]

curry supplier

[thorn hedge]

so by multiplying both sides by -1

we get

$\beta = 48$, $\gamma = -32$

[sand grove]

curry supplier

[thorn hedge]

so our equation looks like this

$\alpha(x + 48)(x - 32)$

[sand grove]

curry supplier

[thorn hedge]

but we dont know what $\alpha$ is right?

[sand grove]

curry supplier

[thorn hedge]

heres where the third coordinate helps us

because we know that it lies on the graph we can subsititute in the x coordinates and solve for alpha

[thorn hedge]

btw the whole equation is $y = \alpha(x + 48)(x - 32)$ ill expand it out later im lazy

[sand grove]

curry supplier

[thorn hedge]

so the third coordinate is (-8,-16)

[thorn hedge]

from this we get y = -16, x = -8

[thorn hedge]

we sub in x = -8 and y = -16to this equaeion

we get

wait

bruh im stupid i didnt need to do allat (-8,-16) is the vertex

BRUH

[thorn hedge]

so we can js write this into vertex form

(vertex form is y = a(x+b)^2 + c)

[thorn hedge]

vertex is (-b, c)

so we know -b = -8 and -16 = c

so the vertex form is y = a(x+8)^2 - 16

get another point so lets use (32,0)

0 = a(32+8)^2 - 16

so that means that

a(1600) - 16 = 0

a(1600) = 16

a = 0.01

i think u misread the coords of the turning point

intstead of (-8,-16) you mustve read (-8,16)

so ye now the equation is y = 0.01(x+8)^2 - 16

expand that out iyw i cba but thats the answer

[still merlin]

@thorn hedge my answer is correct it’s just rather than 0.16x, it was 1.6x but Idk how

@unreal summit

[unreal summit]

it was not, as in 7c the coefficient of x^2 is positive, whereas yours is negative

[still merlin]

@unreal summit prolly I looked at the wrong answer

Aren’t the zeros -48 and 32

[storm kestrel]

@still merlin

:HelpIcon:| Help Reminder

Hello faze_sh3wy, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

[thorn hedge]

no

[storm kestrel]

An error occurred while processing your command. Managers have been notified.

[thorn hedge]

no

[storm kestrel]

An error occurred while processing your command. Managers have been notified.