Question

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

There are no zeros.
There are no zeros.

(−4,0)(−0.5,0)
left parenthesis negative 4 comma 0 right parenthesis left parenthesis negative 0.5 comma 0 right parenthesis

(4,0)(−1,0)
left parenthesis 4 comma 0 right parenthesis left parenthesis negative 1 comma 0 right parenthesis

(0,4)
left parenthesis 0 comma 4 right parenthesis
Remaining Attempts : 3
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Answer 1

To determine the zeros of the quadratic function \( y = 2x^2 + 9x + 4 \), we need to find the values of \( x \) that make \( y = 0 \).

This involves solving the quadratic equation:

\[
2x^2 + 9x + 4 = 0
\]

We can use the quadratic formula to find the roots, which is given by:

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

In this equation:
- \( a = 2 \)
- \( b = 9 \)
- \( c = 4 \)

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

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

Since the discriminant is positive, there are two distinct real roots.

Next, we calculate the roots using the quadratic formula:

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

Calculating \( \sqrt{49} \):

\[
\sqrt{49} = 7
\]

Now, substituting this value back into the formula, we get:

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

Calculating the two potential solutions:

1. For \( -9 + 7 = -2 \):

\[
x_1 = \frac{-2}{4} = -0.5
\]

2. For \( -9 - 7 = -16 \):

\[
x_2 = \frac{-16}{4} = -4
\]

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

\[
(-4, 0) \quad \text{and} \quad (-0.5, 0)
\]

So the correct response is:

**(−4,0)(−0.5,0)**