Re: In the xy-plane, does y=ax^2+bx+c intersect with the x-axis? (1) a>0 (
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24 Sep 2022, 01:21
Solution:
The given equation is of a parabola. Therefore, knowing the values of 'a' and 'c' will tell the position of and direction of the curve.
Statement (I): a>0.
If value of 'a' is positive in a parabola's equation, it means that the parabola opens upward (imagine a big 'U' in the coordinate place) (conversely, if the value of 'a' is negative, the parabola opens downwards).
However, knowing that 'a is positive is not enough as the parabola may well be above the x axis, in which case it never intersects the x-axis.
Insufficient.
Statement 2 - c <0.
This indicates that the 'y intercept of the parabola is negative, i.e., the para bola intersects y axis in the latter's negative territory. However, we don't know whether the parabola is upward or downward.
So insufficient.
Combining I and II:
we know that the parabola is upward opening and it intersects y axis is the latter's negative territory. Therefore, it will interest X axis at two point.
Sufficient.
Solution - C.