Question
determine the x-intercepts of the function that translates the original function f(x) = x^2 down 4 units
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GPT 3.5
To determine the x-intercepts of a function that is obtained by translating the original function f(x) = x^2 down 4 units, we need to find the x-values for which the translated function equals zero.
Let's call the translated function g(x). Since the original function f(x) = x^2 is translated down 4 units, we can express g(x) as: g(x) = x^2 - 4.
Now, let's set g(x) equal to zero to find the x-intercepts: g(x) = x^2 - 4 = 0.
Adding 4 to both sides of the equation: x^2 - 4 + 4 = 0 + 4.
Simplifying the equation: x^2 = 4.
To solve for x, we take the square root of both sides of the equation: √(x^2) = √4.
Taking the square root, we get two possible solutions: x = 2 and x = -2.
Therefore, the x-intercepts of the translated function g(x) = x^2 - 4 are x = 2 and x = -2.
Let's call the translated function g(x). Since the original function f(x) = x^2 is translated down 4 units, we can express g(x) as: g(x) = x^2 - 4.
Now, let's set g(x) equal to zero to find the x-intercepts: g(x) = x^2 - 4 = 0.
Adding 4 to both sides of the equation: x^2 - 4 + 4 = 0 + 4.
Simplifying the equation: x^2 = 4.
To solve for x, we take the square root of both sides of the equation: √(x^2) = √4.
Taking the square root, we get two possible solutions: x = 2 and x = -2.
Therefore, the x-intercepts of the translated function g(x) = x^2 - 4 are x = 2 and x = -2.