Question

The graphs below have the same shape. What is the equation of the blue

graph?
g(x) =
f(x) = x²
-5
Xa
A. g(x)=x²-4
B. g(x) = x² + 4
OC. g(x) = (x-4)²
OD. g(x) = (x+4)²
g(x) = ?
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Answer 1

Since the blue graph has the same shape as the function f(x) = x², we can conclude that the equation of the blue graph is a transformation of the function f(x) = x². By analyzing the provided options, we can determine the correct equation by identifying the transformation applied to the function f(x) = x².

The graph is shifted horizontally by 4 units to the left. To achieve this transformation, we need to shift the function f(x) = x² four units to the left, which is represented as (x - 4)².

Therefore, the equation of the blue graph is:
g(x) = (x - 4)²

Hence, the correct option is C. g(x) = (x - 4)².

Answer 2

IG: yiimbert

The blue graph is obtained by shifting the graph of the quadratic function f(x) = x^2 to the right by 4 units. Therefore, the equation of the blue graph is of the form:

g(x) = (x - a)^2 + b

where a is the shift value and b is the y-intercept value. In this case, a = 4 since the graph is shifted to the right by 4 units, and b = -5 since the graph intersects the y-axis at the point (0, -5).

Therefore, the equation of the blue graph is:

g(x) = (x - 4)^2 - 5

So, the correct answer is option C: g(x) = (x-4)^2.