Respuesta :
Answer:
[tex]y=2(x+\frac{7}{2})^2+\frac{1}{2}[/tex] vertex form
Step-by-step explanation:
[tex]y = (x + 3)^2 + (x + 4)^2[/tex]
Lets square the terms
[tex](x+3)^2=x^2+6x+9[/tex]
[tex](x+4)^2= x^2+8x+16[/tex]
[tex]y = x^2+6x+9 +x^2+8x+16=2x^2+14x+25[/tex]
Now use completing the square method to get the vertex form
to apply the method we need to take out 2
WE take middle term , divide it by 2 and square it . then add and subtract it
[tex]y =2(x^2+7x)+25[/tex]
[tex]\frac{7}{2}[/tex]
square it [tex]\frac{49}{4}[/tex]
Add and subtract the fraction
[tex]y=2(x^2+7x+\frac{49}{4}-\frac{49}{4})+25[/tex]
Take out -49/4 and multiply with 2 , then add it with 25
[tex]y=2(x^2+7x+\frac{49}{4})-\frac{49}{2}+25[/tex]
[tex]y=2(x^2+7x+\frac{49}{4})+\frac{1}{2}[/tex]
[tex]y=2(x+\frac{7}{2})^2+\frac{1}{2}[/tex]
