Question

Draw a diagram to show that there are two tangent lines to the parabola y = x^2 that pass through the point (0,-4). FIND THE COORDINATES of the points where these tangent lines intersect the parabola.

Answer 1

The slope of the tangent line will be 2x
Equation of tangent line that passes through (0,-4)
point-slope
y+4=2x(x-0)
y=2x^2-4
Now we find the intersections:
2x^2-4=x^2
x^2-4=0
x= +/-2
(2, 4), (-2, 4)

Answer 2

why'd you take out the 2 where'd it go

Answer 3

2x^2-4=x^2
subtract x^2 from both sides

Answer 4

so you'll have 2 tangent lines, with a slope of 2(2)=4, and 2(-2)=-4, passing through the point (0,-4)
so the equation of the lines will be y=4x-4 and y=-4x-4

Answer 5

yeah sorry got it