https://file.aiquickdraw.com/mathbot/file/1724969390170m2wu7bpe.jpg

What numbers will represent a solution to the function above

The function given in the image is:

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

This is a quadratic function. To find a solution (or the value of \(x\)) that satisfies the equation \(f(x) = 0\), we set the function equal to zero and solve for \(x\):

\[
x^2 + 5 = 0
\]

Subtract 5 from both sides:

\[
x^2 = -5
\]

Now, take the square root of both sides:

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

Since the square root of a negative number is not a real number, the solutions are complex numbers:

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

Therefore, the solutions to the function \(f(x) = 0\) are \(x = i\sqrt{5}\) and \(x = -i\sqrt{5}\).

Would you like more details on this, or do you have any questions?

Here are some related questions:
1. What is the domain and range of the function \(f(x) = x^2 + 5\)?
2. How do you graph the function \(f(x) = x^2 + 5\)?
3. What is the vertex of the parabola represented by \(f(x) = x^2 + 5\)?
4. What does the discriminant tell us about the solutions of a quadratic equation?
5. How can you solve quadratic equations using the quadratic formula?

**Tip:** When dealing with quadratic equations, always consider whether the discriminant (the part under the square root in the quadratic formula) is positive, negative, or zero. This will tell you if the solutions are real, complex, or repeated.

Learn how to solve the quadratic function x^2 + 5 = 0 with complex number solutions. This problem covers quadratic equations, complex numbers, and the quadratic formula. Suitable for students in Grades 10-12.

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