https://file.aiquickdraw.com/mathbot/file/1724969454109fhib4qwf.jpg

What numbers will represent a solution to the function above

The function in the image is:

\[
f(x) = x^2 + 5
\]

To find the numbers (values of \(x\)) that represent a solution to the function, we set the function equal to zero and solve for \(x\):

\[
x^2 + 5 = 0
\]

Subtract 5 from both sides:

\[
x^2 = -5
\]

Taking the square root of both sides gives:

\[
x = \pm \sqrt{-5}
\]

Since the square root of a negative number is imaginary, the solutions are:

\[
x = \pm i\sqrt{5}
\]

Thus, the solutions to the equation \(f(x) = 0\) are \(x = i\sqrt{5}\) and \(x = -i\sqrt{5}\), which are complex numbers.

Would you like further details or have any additional questions?

Here are some related questions:
1. What is the vertex of the parabola given by \(f(x) = x^2 + 5\)?
2. How do you determine the axis of symmetry for this quadratic function?
3. Can the function \(f(x) = x^2 + 5\) ever have real solutions?
4. How do you calculate the minimum value of \(f(x)\)?
5. What is the general form of a quadratic function?

**Tip:** When dealing with quadratic functions, remember that the sign of the discriminant (the part inside the square root in the quadratic formula) determines whether the solutions are real or complex.

Discover the solutions to the quadratic function f(x) = x^2 + 5. Learn how to solve complex numbers in quadratic equations. Suitable for advanced high school students studying quadratic equations and complex numbers.

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