Question

Make predictions about how many times the graph of each equation below will touch the x axis. You may first want to rewrite some of the equations in a more useful form.=(x-2)(x-3).
A. y=(x+1)^2

B. y=x^2+6x+9

C. y=x^2+7x+10

D. y=x^2+6x+8

E. y=-x^2-4x-4

Answer 1

A, Not really. That first parabola has its vertex right on the x axis at x = -1 so it only hits the axis there

B, = (x+3)(x+3), same deal, vertex on x axis at x = -3 so barely touches once

C. b^2-4ac = 49-40 so yes, hits twice

D. b^2-4ac = 36-32 yes again hits twice
(x+4)(x+2)
E. b^2-4ac = 16+16 so yes, twice again
(x-2)(x+2) at +2 and -2

Answer 2

Thank you

Answer 3

You are welcome.