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The graphs below have the same shape. What is the equation of the blue
graph?
G(X)=?
F(X) = x²
G(x) =
-6
OA. G(x)=(x+4)²+1
B. G(x) = (x-4)²+1
OC. G(x)=(x+4)²-1
D. G(x) = (x-4)²-1
5

The graphs below have the same shape What is the equation of the blue graph GX FX x Gx 6 OA Gxx41 B Gx x41 OC Gxx41 D Gx x41 5 class=


Answer :

Answer:

A. G(X) = (x + 4)² + 1

Step-by-step explanation:

We can find the equation of the blue graph by using these principles:

For quadratic function [tex]f(x)=a(x+p)^2+q[/tex]:

  • If the graph is moved m units to the left, then the function will become [tex]f(x)=a(x+(p+m))^2+q[/tex]
  • If the graph is moved m units to the right, then the function will become [tex]f(x)=a(x+(p-m))^2+q[/tex]
  • If the graph is moved n units to the top, then the function will become [tex]f(x)=a(x+p)^2+(q+n)[/tex]
  • If the graph is moved n units to the bottom, then the function will become [tex]f(x)=a(x+p)^2+(q-n)[/tex]

Given:

  • [tex]F(X)=x^2[/tex]

                [tex]=1(x+0)^2+0[/tex]

  • [tex]G(X)[/tex] is [tex]F(X)[/tex] that is move 4 units to the left and 1 units to the top

Therefore:

[tex]G(X)=1(x+4)^2+1[/tex]

[tex]\bf G(X)=(x+4)^2+1[/tex]

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