https://file.aiquickdraw.com/mathbot/file/1726427826218rht1wmi5.jpg

Let's go through the math problem shown in the image.

We are given the function \( y = f(x) = x^2 + 5 \). There are four parts to the problem:

### (a) Find the value of \( y \) when \( x = 0 \):
Substituting \( x = 0 \) into the equation:

\[
y = 0^2 + 5 = 5
\]

So, the value of \( y \) when \( x = 0 \) is \( 5 \).

### (b) What is \( f(4) \)?
Substituting \( x = 4 \) into the equation:

\[
f(4) = 4^2 + 5 = 16 + 5 = 21
\]

So, \( f(4) = 21 \).

### (c) What values of \( x \) give \( y \) a value of \( 9 \)?
We are solving for \( x \) when \( y = 9 \). So, we set \( x^2 + 5 = 9 \) and solve for \( x \):

\[
x^2 + 5 = 9
\]
\[
x^2 = 9 - 5 = 4
\]
\[
x = \pm \sqrt{4} = \pm 2
\]

So, the values of \( x \) are \( -2 \) and \( 2 \).

### (d) Are there any values of \( x \) that give \( y \) a value of \( 1 \)?
We are solving for \( x \) when \( y = 1 \). Set \( x^2 + 5 = 1 \):

\[
x^2 + 5 = 1
\]
\[
x^2 = 1 - 5 = -4
\]

Since \( x^2 = -4 \) has no real solutions (because the square of a real number cannot be negative), there are no real values of \( x \) that give \( y = 1 \).

It seems like your answer to part (c) is correct but maybe incomplete in some detail on the platform, so double-check if the formatting or additional explanations are needed.

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Would you like more details or have any questions about this?

Here are 5 related questions you might find useful:
1. What are the roots of the equation \( x^2 + 3x + 2 = 0 \)?
2. Can you solve \( x^2 - 16 = 0 \) for \( x \)?
3. How do you graph \( y = x^2 + 5 \) and what does the graph look like?
4. What happens to the graph of \( y = x^2 + c \) as \( c \) increases or decreases?
5. What are imaginary solutions, and how do they apply to equations like \( x^2 + 4 = 0 \)?

**Tip**: When solving quadratic equations, check if you can factor or use the square root method before trying other techniques like the quadratic formula.

Let y = f(x) = x^2 + 5. (a) Find the value of y when x is zero. (b) What is f(4)? (c) What values of x give y a value of 9? (d) Are there any values of x that give y a value of 1?

Learn how to solve the quadratic function f(x) = x^2 + 5 to find specific values of y when x is given. This problem covers algebraic concepts, including quadratic functions and solving for roots. Suitable for students in Grades 8-10.

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