Answer:
[tex]g(x)=(x-4)^2+1[/tex]
Step-by-step explanation:
The graph is shifted 4 to the right and 1 up. When a graph is moving left or right, the sign switches. Right means -, left means +.
The equation of the blue graph is g(x) = (x+4)² - 2
A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
parabola, open curve, a conic segment produced via the intersection of a proper circular cone and a plane parallel to an element of the cone.
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to the function
If shift down by 4 units, subtract 4 from the function
x+4 because adding 4 to the x coordinate would shift it over 4
y+2 because adding 2 to the y coordinate would shift it up 2
⇒ g(f(x)) = ( x+4, y +2 )
⇒ g(x) + 2 = (x+4)²
Hence, the equation of the blue graph is g(x) = (x+4)² - 2
Learn more about parabola here:
brainly.com/question/4074088
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