We can answer everything either from the graph or
from the equation and the disriminant.
1) has a maximum value because a > 0
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.
2) has a negative y - intercept
If c > 0 the graph has a positive y-intercept
If c < 0 the graph has a negative y-intercept
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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
3) has no intercepts on the x-axis
That is true because the discriminant < 0
4)has a discriminant that is more then zero
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
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