![\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis}](https://tex.z-dn.net/?f=%5Cbf%20~%5Chspace%7B10em%7D%5Ctextit%7Bfunction%20transformations%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20f%28x%29%3D%20A%28%20Bx%2B%20C%29%5E2%2B%20D%20%5C%5C%5C%5C%20f%28x%29%3D%20A%5Csqrt%7B%20Bx%2B%20C%7D%2B%20D%20%5C%5C%5C%5C%20f%28x%29%3D%20A%28%5Cmathbb%7BR%7D%29%5E%7B%20Bx%2B%20C%7D%2B%20D%20%5Cend%7Barray%7D%5Cqquad%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20f%28x%29%3D%5Ccfrac%7B1%7D%7BA%28Bx%2BC%29%7D%2BD%20%5C%5C%5C%5C%5C%5C%20f%28x%29%3D%20A%20sin%5Cleft%28%20B%20x%2B%20C%20%5Cright%29%2B%20D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20stretches%20or%20shrinks%20horizontally%20by%20%7D%20A%5Ccdot%20B%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20flips%20it%20upside-down%20if%20%7D%20A%5Ctextit%7B%20is%20negative%7D%5C%5C%20~~~~~~%5Ctextit%7Breflection%20over%20the%20x-axis%7D)
![\bf \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbullet%20%5Ctextit%7B%20flips%20it%20sideways%20if%20%7D%20B%5Ctextit%7B%20is%20negative%7D%5C%5C%20~~~~~~%5Ctextit%7Breflection%20over%20the%20y-axis%7D%20%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20horizontal%20shift%20by%20%7D%5Cfrac%7B%20C%7D%7B%20B%7D%5C%5C%20~~~~~~if%5C%20%5Cfrac%7B%20C%7D%7B%20B%7D%5Ctextit%7B%20is%20negative%2C%20to%20the%20right%7D%5C%5C%5C%5C%20~~~~~~if%5C%20%5Cfrac%7B%20C%7D%7B%20B%7D%5Ctextit%7B%20is%20positive%2C%20to%20the%20left%7D%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20vertical%20shift%20by%20%7D%20D%5C%5C%20~~~~~~if%5C%20D%5Ctextit%7B%20is%20negative%2C%20downwards%7D%5C%5C%5C%5C%20~~~~~~if%5C%20D%5Ctextit%7B%20is%20positive%2C%20upwards%7D%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20period%20of%20%7D%5Cfrac%7B2%5Cpi%20%7D%7B%20B%7D)
with that template in mind, let's see
down by 5 units, D = -5
to the left by 4 units, C = +4
![\bf G(x)=x^2\implies G(x)=1(1x+\stackrel{C}{0})^2+\stackrel{D}{0} \\\\\\ \begin{cases} D=-5\\ C=+4 \end{cases}\implies F(x)=1(1x+\stackrel{C}{4})^2\stackrel{D}{-5}\implies F(x)=(x+4)^2-5](https://tex.z-dn.net/?f=%5Cbf%20G%28x%29%3Dx%5E2%5Cimplies%20G%28x%29%3D1%281x%2B%5Cstackrel%7BC%7D%7B0%7D%29%5E2%2B%5Cstackrel%7BD%7D%7B0%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20D%3D-5%5C%5C%20C%3D%2B4%20%5Cend%7Bcases%7D%5Cimplies%20F%28x%29%3D1%281x%2B%5Cstackrel%7BC%7D%7B4%7D%29%5E2%5Cstackrel%7BD%7D%7B-5%7D%5Cimplies%20F%28x%29%3D%28x%2B4%29%5E2-5)
Answer:
this is what I found:
9
Step-by-step explanation:
mark brainliest please :)
Answer:
Step-by-step explanation:
(x-3)²-4=0
(x-3)²=4=2²
x-3=±2
x=3±2
x=3-2,3+2
x=1,5
it has two distinct roots and a vertex at x=3
Answer:
Breadth=x+2
Step-by-step explanation:
![Solution,\\\\Length(l)=5m\\\\Area=5x+10m^{2} \\\\Breadth(b)=?\\\\As,\\\\Area=l*b\\\\5x+10=5*b\\\\b=\frac{5x+10}{5}\\\\b=\frac{5x}{5} +\frac{10}{5} \\\\b=x+2](https://tex.z-dn.net/?f=Solution%2C%5C%5C%5C%5CLength%28l%29%3D5m%5C%5C%5C%5CArea%3D5x%2B10m%5E%7B2%7D%20%5C%5C%5C%5CBreadth%28b%29%3D%3F%5C%5C%5C%5CAs%2C%5C%5C%5C%5CArea%3Dl%2Ab%5C%5C%5C%5C5x%2B10%3D5%2Ab%5C%5C%5C%5Cb%3D%5Cfrac%7B5x%2B10%7D%7B5%7D%5C%5C%5C%5Cb%3D%5Cfrac%7B5x%7D%7B5%7D%20%2B%5Cfrac%7B10%7D%7B5%7D%20%5C%5C%5C%5Cb%3Dx%2B2)