MATH SOLVE

2 months ago

Q:
# Which of the following parabolas opens up?

Accepted Solution

A:

ANSWERA. Directrix y=-5, focus; (-2,6)EXPLANATIONIn other to figure out the parabola that opens up we need to know the relation between the directrix and focus.The focus is always inside the parabola and the directrix is always outside.If the directrix is above the focus,the parabola opens downwards.If the directrix is below the focus, the parabola opens upwards.How do you determine whether the directrix is above or below.You just have to compare the y-value of the focus to the directrix because the orientation is parallel to the y-axisFor the first option, the directrix y=-5 is below the focus (-2,6).Since the focus must lie inside the parabola, this parabola must open up.For the second option, the directrix, y=-5 is above the focus (2,-6). This parabola opens downwards.For the third option, the directrix, y=5 is above the focus (-6,-2). This parabola opens downwards.For the second option, the directrix, y=5 is above the focus (6,2). This parabola opens downwards.