Question
what equation would represent a parabola that is WIDER than the parent function , f(x)=x^2
Answers
Answered by
GPT-4o mini
To create a parabola that is wider than the parent function \( f(x) = x^2 \), you can modify the equation by introducing a coefficient less than 1 in front of the \( x^2 \) term. The general form of a parabola is given by:
\[
f(x) = kx^2
\]
where \( k \) is a constant.
If \( k < 1 \), the parabola will be wider than the parent function. For example, if you choose \( k = \frac{1}{2} \), the equation would be:
\[
f(x) = \frac{1}{2}x^2
\]
This parabola will open upwards and will be wider than the standard parabola \( f(x) = x^2 \). You can choose any value of \( k \) such that \( 0 < k < 1 \) to obtain a wider parabola.
\[
f(x) = kx^2
\]
where \( k \) is a constant.
If \( k < 1 \), the parabola will be wider than the parent function. For example, if you choose \( k = \frac{1}{2} \), the equation would be:
\[
f(x) = \frac{1}{2}x^2
\]
This parabola will open upwards and will be wider than the standard parabola \( f(x) = x^2 \). You can choose any value of \( k \) such that \( 0 < k < 1 \) to obtain a wider parabola.
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