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Question 6 of 10
If you apply the changes below to the quadratic parent function, fx) = x?
what is the equation of the new function?
.
• Shift 1 unit right.
Vertically stretch by a factor of 5.
• Reflect over the x-axis.
O A. gx) = 5x2-1
=
O B. g(x) = -5(x + 1)2
O C. g(x) = -5(x - 1)2
D. g(x) = (-5x + 1)2

Sagot :

Answer:

The correct option is C.

Step-by-step explanation:

The quadratic parent function is

[tex]f(x)=x^2[/tex]

The translation is defined as

[tex]g(x)=k(x+a)^2+b[/tex]                 .... (1)

Where, k is vertical stretch, a is horizontal shift and b is vertical shift.

If |k|>1, then graph of parent function stretch vertically by factor |k| and if 0<|k|<1, then parent function compressed vertically by factor |k|. Negative k represents the reflection across x axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The graph shift 1 unit right,vertically stretch by a factor of 5 , reflect over the x-axis. So, a=-1, |k|=5 and k=-5

Substitute a=-1 and k=5 in equation (1).

[tex]g(x)=-5(x+(-1))^2+(0)[/tex]

[tex]g(x)=-5(x-1)^2[/tex]

Therefore the correct option is C.

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