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# The graph is that of $$y = 2x^2 - 5x - 3.$$ For what value of $$x$$ will $$y$$ b...

### Question

The graph is that of $$y = 2x^2 - 5x - 3.$$ For what value of $$x$$ will $$y$$ be negative? For what value of $$x$$ will $$y$$ be negative?

### Options

A)
$$-\frac{1}{2} \leq x < 3$$
B)
$$-\frac{1}{2} < x \leq 3$$
C)
$$-\frac{1}{2} < x < 3$$
D)
$$-\frac{1}{2} \leq x \leq 3$$

### Explanation:

The graph is that of $$y = 2x^2 - 5x - 3.$$

$$2x^2 - 5x - 3 = 0$$
$$2x^2 - 6x + x - 3 = 0$$
$$2x(x - 3) + 1(x - 3) = 0$$
$$(2x + 1)(x - 3) = 0$$
$$2x + 1 = 0$$
$$2x = -1$$
$$x = -\frac{1}{2}$$
$$x - 3 = 0$$
$$x = 3$$
For what value of $$x$$ will $$y$$ be negative?
$$-\frac{1}{2} < x < 3$$

## Dicussion (1)

• The graph is that of $$y = 2x^2 - 5x - 3.$$

$$2x^2 - 5x - 3 = 0$$
$$2x^2 - 6x + x - 3 = 0$$
$$2x(x - 3) + 1(x - 3) = 0$$
$$(2x + 1)(x - 3) = 0$$
$$2x + 1 = 0$$
$$2x = -1$$
$$x = -\frac{1}{2}$$
$$x - 3 = 0$$
$$x = 3$$
For what value of $$x$$ will $$y$$ be negative?
$$-\frac{1}{2} < x < 3$$