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.

1 answer

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:

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