To find the zeros of the quadratic function \( y = 2x^2 + 7x \), we need to set the equation equal to zero and solve for \( x \):
\[ 2x^2 + 7x = 0 \]
First, we can factor out the common term \( x \):
\[ x(2x + 7) = 0 \]
This gives us two factors to solve:
- \( x = 0 \)
- \( 2x + 7 = 0 \)
Now, let's solve the second equation:
\[ 2x + 7 = 0 \implies 2x = -7 \implies x = -\frac{7}{2} \]
Thus, the two solutions (or zeros) of the equation are:
- \( x = -\frac{7}{2} \)
- \( x = 0 \)
Listing the smaller solution first, the zeros of the function \( y = 2x^2 + 7x \) are:
\[ -\frac{7}{2}, 0 \]