Question

Determine the zero(s) of the quadratic function y=2x2+9x+4 .(1 point) Responses (4,0)(−1,0) open paren 4 comma 0 close paren times open paren negative 1 comma 0 close paren - incorrect (−4,0)(−0.5,0) open paren negative 4 comma 0 close paren times open paren negative 0 point 5 comma 0 close paren - no response given (0,4) open paren 0 comma 4 close paren - no response given There are no zeros.

Answer 1

To find the zeros of the quadratic function \(y = 2x^2 + 9x + 4\), we can use the quadratic formula:

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

In this case, the coefficients are:
- \(a = 2\)
- \(b = 9\)
- \(c = 4\)

First, we calculate the discriminant (\(b^2 - 4ac\)):

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

Now we can apply the quadratic formula:

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

This gives us two potential solutions:

1. For the plus sign:

\[
x = \frac{-9 + 7}{4} = \frac{-2}{4} = -0.5
\]

2. For the minus sign:

\[
x = \frac{-9 - 7}{4} = \frac{-16}{4} = -4
\]

Therefore, the zeros of the function \(y = 2x^2 + 9x + 4\) are \((-4, 0)\) and \((-0.5, 0)\).

The correct response from your options is:
\[
(-4, 0) \text{ and } (-0.5, 0)
\]