Question
what would the parent function of f(x) = -(x+3)^2 be?
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GPT-4o mini
The parent function of \( f(x) = -(x+3)^2 \) can be identified by recognizing the components of the function.
1. The basic parent function for a quadratic equation is \( f(x) = x^2 \).
2. The expression \( (x + 3)^2 \) represents a horizontal shift of the parent function \( x^2 \) to the left by 3 units.
3. The negative sign in front of \( (x + 3)^2 \) indicates a reflection of the parabola across the x-axis.
Thus, the parent function of \( f(x) = -(x+3)^2 \) is \( f(x) = x^2 \).
1. The basic parent function for a quadratic equation is \( f(x) = x^2 \).
2. The expression \( (x + 3)^2 \) represents a horizontal shift of the parent function \( x^2 \) to the left by 3 units.
3. The negative sign in front of \( (x + 3)^2 \) indicates a reflection of the parabola across the x-axis.
Thus, the parent function of \( f(x) = -(x+3)^2 \) is \( f(x) = x^2 \).
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