Question

determine the zeros in y = -5x^2
+ 16x

Answer 1

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

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

Next, we can factor the equation:

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

This gives us two factors that we can set to zero:

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

Now we solve the second equation:

\[
-5x + 16 = 0 \implies -5x = -16 \implies x = \frac{16}{5} = 3.2
\]

Thus, the zeros of the function are:

\[
x = 0 \quad \text{and} \quad x = 3.2
\]

So the function \( y = -5x^2 + 16x \) has zeros at \( x = 0 \) and \( x = 3.2 \).