The vertex of the parabola below is at the point (1, 5), and the point (2, 8) is on the parabola. What is the equation of the parabola? A. y = 2(x – 1)2 + 5 B. y = 3(x + 1)2 + 5 C. y = 3(x – 1)2 + 5 D. y = 2(x + 1)2 + 5

B

Step-by-step explanation:

the parabola having (1,5) as vertex have as equation:

y=k*(x-1)²+5

It is passing through (2,8)

8=k*(2-1)²+5 ==> k+5=8 ==> k=3

equation is  y=3(x-1)²+5

Answer B

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!