Question

How many times does the parabola `y= 3x^2 + 4x - 5` intersect the line `y= -6`?

Answer 1

twice, at points `(-1,-6)` and `(-1/3,-6)`

Explanation:

putting y = -6 in the given equation of the parabola we have
`3x^2+4x-5=-6`
`=>3x^2+4x-5+6=0`
`=>3x^2+4x+1=0`
`=>3x^2+3x+x+1=0`
`=>3x(x+1)+1(x+1)=0`
`=>(x+1)(3x+1)=0`
`:.x=-1 and x=-1/3`
point of intersections are
`(-1,-6)` and `(-1/3,-6)`