Question 985860
<pre>
{{{y = 2x^2+x+7}}}

We can answer everything either from the graph or
from the equation and the disriminant.
</pre>
1) has a maximum value because a > 0
<pre>
If a quadratic equation has a > 0 it opens upward and has a minimum value.
If a quadratic equation has a < 0 it opens downward and has a maximum value.

So (1) is false.
</pre>
2)  has a negative y - intercept
<pre>
If c > 0  the graph has a positive y-intercept
If c < 0  the graph has a negative y-intercept  

---------------
The others depend on the discriminant:

If discriminant > 0 there are two x-intercepts
If discriminant = 0 there is one x-intercept
If discriminant < 0 there are no x-intercepts

Discriminant = b²-4ac = 1²-4(2)(7) = 1-56 = -55

</pre>
3) has no intercepts on the x-axis
<pre>
That is true because the discriminant < 0
</pre>
4)has a discriminant that is more then zero
<pre>
That's false because discriminant = -55

So the only correct answer is 3.

Let's graph it.

 x | y
-3 | 22
-2 | 13
-1 | 8
 0 | 7
 1 | 10
 2 | 17

{{{drawing(3200/7,400,-4,2,-2,25, graph(3200/7,400,-4,2,-2,25,2x^2+x+7),

circle(-3,22,0.09),circle(-3,22,0.07),circle(-3,22,0.05),circle(-3,22,0.03),circle(-3,22,0.01),

circle(-2,13,0.09),circle(-2,13,0.07),circle(-2,13,0.05),circle(-2,13,0.03),circle(-2,13,0.01),

circle(-1,8,0.09),circle(-1,8,0.07),circle(-1,8,0.05),circle(-1,8,0.03),circle(-1,8,0.01),

circle(0,7,0.09),circle(0,7,0.07),circle(0,7,0.05),circle(0,7,0.03),circle(0,7,0.01),

circle(1,10,0.09),circle(1,10,0.07),circle(1,10,0.05),circle(1,10,0.03),circle(1,10,0.01),

circle(2,17,0.09),circle(2,17,0.07),circle(2,17,0.05),circle(2,17,0.03),circle(2,17,0.01)




)}}}

So from the graph we can tell: 
It has a minimum value.
It has a positive y-intercept.
It has no intercepts on the x-axis.

Edwin</pre>