Draw a diagram to show that there are two tangent lines to the parabola of y = x^2 that pass through the point (0, −9).

Question

Draw a diagram to show that there are two tangent lines to the parabola of y = x² that passes through the point (0, −9).

Find the coordinates of the points where these tangent lines intersect the parabola.

Smaller (x,y) value=

Larger (x,y) value =

Answer 1

y=6x -9 and y=-6x -9 intersect the parabola at (3,9) and (-3,9)

slopes of the tangent lines are 6 and -6

slope of the parabola = the derivative of y=x^2 which is y'=2x

at the point (3,9) the slope = 2(3) = 6, at the point (-3,9) the slope = 2(-3) = -6

larger (x,y) = (3,9)

smaller (x,y) = (-3,9)

they're symmetric about the axis of symmetry x=0