Question

Determine the zero of the quadratic function y = -5x^2 + 16x

Answer 1

To find the zeros of the quadratic function \( y = -5x^2 + 16x \), we need to set the function equal to zero:

\[
-5x^2 + 16x = 0
\]

Next, we can factor out \( x \) from the equation:

\[
x(-5x + 16) = 0
\]

Now, we have two factors that can be set to zero:

1. \( x = 0 \)
2. \( -5x + 16 = 0 \)

For the second factor, we can solve for \( x \):

\[
-5x + 16 = 0
\]

Rearranging gives:

\[
-5x = -16
\]

Dividing both sides by -5:

\[
x = \frac{16}{5}
\]

Thus, the zeros of the quadratic function are:

\[
x = 0 \quad \text{and} \quad x = \frac{16}{5}
\]

In summary, the zeros of the quadratic function \( y = -5x^2 + 16x \) are \( x = 0 \) and \( x = \frac{16}{5} \).