Question

Quadratic Equations Online Practice
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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

(0,4)
left parenthesis 0 comma 4 right parenthesis

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

Answer 1

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

We can use the quadratic formula:

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

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

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

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

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

Now we substitute the values into the quadratic formula:

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

Now we have two solutions to compute:

1. \(x = \frac{{-9 + 7}}{4} = \frac{{-2}}{4} = -0.5\)
2. \(x = \frac{{-9 - 7}}{4} = \frac{{-16}}{4} = -4\)

Thus the zeros of the quadratic function are:

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

So the correct response is:

**(−4,0)(−0.5,0)**