Question

Determine the zero(s) of the quadratic function y=2x2+9x+4
.(1 point)
Responses

Answer 1

To determine the zeros of the quadratic function \( y = 2x^2 + 9x + 4 \), we can use the quadratic formula, which is given by:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

where \( a = 2 \), \( b = 9 \), and \( c = 4 \).

First, we need to calculate the discriminant (\( D \)):

\[
D = b^2 - 4ac = 9^2 - 4 \cdot 2 \cdot 4
\]
\[
D = 81 - 32 = 49
\]

Since the discriminant is positive, there will be two distinct real zeros.

Next, we can substitute the values into the quadratic formula:

\[
x = \frac{-9 \pm \sqrt{49}}{2 \cdot 2}
\]
\[
x = \frac{-9 \pm 7}{4}
\]

Now we will calculate the two potential values for \( x \).

1. **First solution:**
\[
x = \frac{-9 + 7}{4} = \frac{-2}{4} = -\frac{1}{2}
\]

2. **Second solution:**
\[
x = \frac{-9 - 7}{4} = \frac{-16}{4} = -4
\]

Thus, the zeros of the quadratic function \( y = 2x^2 + 9x + 4 \) are:

\[
x = -\frac{1}{2} \quad \text{and} \quad x = -4
\]