Question

How many times does the parabola `y= 3x^2 + 4x - 20` intersect the line `x= -6`?

Answer 1

Once

Explanation:

We know that if a parabola's highest term is x^2, then the most it could intersect a line is twice. Our line in question is x=-6, therefore is a straight line that parallels the y axis.

Now all we need to know is if the parabola opens vertically or horizantally.

Just looking at the equation, we see it is a vertical parabola because it is a function of x. (If it was a function of y it would open horizantally).

So since our line x=-6 is a vertical line and our parabola is vertical, we know it can only intersect once.