Question
y = x^2+4x+3 if it had a concave down instead
Answers
GPT-4o mini
To transform the given function \( y = x^2 + 4x + 3 \), which is a quadratic function that opens upwards (concave up), into a concave down function, we need to negate the leading coefficient of the quadratic term.
The original function can be represented in vertex form by completing the square, but for simplicity, we can simply modify the leading coefficient.
The original function is:
\[
y = x^2 + 4x + 3
\]
To make it concave down, we can multiply the entire function by \(-1\):
\[
y = -1(x^2 + 4x + 3)
\]
This gives us:
\[
y = -x^2 - 4x - 3
\]
In this case, \(-x^2 - 4x - 3\) is a concave down quadratic function, as the leading coefficient of the \(x^2\) term is negative.
So, the concave down version of the original function is:
\[
y = -x^2 - 4x - 3
\]
The original function can be represented in vertex form by completing the square, but for simplicity, we can simply modify the leading coefficient.
The original function is:
\[
y = x^2 + 4x + 3
\]
To make it concave down, we can multiply the entire function by \(-1\):
\[
y = -1(x^2 + 4x + 3)
\]
This gives us:
\[
y = -x^2 - 4x - 3
\]
In this case, \(-x^2 - 4x - 3\) is a concave down quadratic function, as the leading coefficient of the \(x^2\) term is negative.
So, the concave down version of the original function is:
\[
y = -x^2 - 4x - 3
\]