Question

For what values of K will the line intersect with the parabola at only one point

3x+k=y
-4x^2-2x+3=y

Answer 1

One is a parabola and one is a straight line how can I find one point of intersection?

Answer 2

3x+k=-4x^2-2x+3
You want this to be true for only one x, thus your discriminant must be 0.

Answer 3

Let's rewrite this equation and simplify it a bit:
4x^2+2x+3x+k-3=4x^2+5x+(k-3)

Answer 4

Discriminant is:
D = b^2-4ac = 25 - 4 * 4 * (k-3)

Answer 5

It must be equal to 0, so:
25-16k+48=0
-16k = -48-25
-16k = -73
k = 73/16... and then just simplify and make sure i didn't make any mistakes

Answer 6

the answer was 5?

Answer 7

-5

Answer 8

u are right its just that instead of -4x^2 its -2x^2

Answer 9

2x^2 <--------------

Answer 10

@bahrom7893 dude you rock the steps you showed me gave me the right answer it was my error placing a wrong digit on one of the equations ;P

Answer 11

Another way to do it, would be to find the minimum value of the parabola - the vertex.

Then plug in that point into the linear equation, to find k.

Answer 12

Cheers :D

Answer 13

Actually nm what i said... that won't necessarily work.