Question

Drag numbers to the lines to show the zeros of the function f of x equals negative x squared plus 9 x minus 20.

Response area with 2 blank spaces
x equals
Blank space 1 empty
and x equals
Blank space 2 empty
Answer options with 8 options.

Answer 1

To find the zeros of the function \( f(x) = -x^2 + 9x - 20 \), we need to solve the equation:

\[
-x^2 + 9x - 20 = 0
\]

We can multiply through by -1 to simplify it:

\[
x^2 - 9x + 20 = 0
\]

Next, we can factor the quadratic:

\[
(x - 4)(x - 5) = 0
\]

Setting each factor to zero gives us the solutions:

\[
x - 4 = 0 \quad \Rightarrow \quad x = 4
\]
\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]

Thus, the zeros of the function are \( x = 4 \) and \( x = 5 \).

Now you can fill in the blanks:

- **Blank space 1**: 4
- **Blank space 2**: 5

So the final answer is:

\[
x = 4 \quad \text{and} \quad x = 5
\]