Quadratic Equations Online Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
18 of 2018 of 20 Items

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)