Question

Can you explain how to solve this?

Answer 1

what do you do to find the point of intersection ?

Answer 2

For linear we can use substitution or elimination but im not sure for this

Answer 3

Try completing the square to get in vertex form?

Answer 4

we solve the equations simultaneously.
so, here we'll have x^2-6x+14 = -x^2-20x-k
and here, 'x' will have a repeated root.

this is one of the many ways of solving it...

Answer 5

a quadratic equation has repeated root when b^2-4ac = 0

Answer 6

Yea I understand that when the descriminat is 0 there is one intercept

Answer 7

do u need the vertex method to solve this ? or any method will do ?

Answer 8

hmm, I guess we can try vertex

Answer 9

then i would let @phi or @wio continue :)

Answer 10

what way were you going to shiw?

Answer 11

I got the vertex form s and I got

(x-3)^2+6

and


-(x-10)^2-k+100

Answer 12

x^2-6x+14 = -x^2-20x-k
bring it in the form ax^2+bx+c=0
then use b^2=4ac to find k

Answer 13

@hartnn can you show that way

Answer 14

so we want to find when it has one rooot/ but how can we find k like this?\

Answer 15

x^2-6x+14 = -x^2-20x-k
2x^2+14x+14+k=0
a=2
b=14
c=14+k
b^2=4ac
14^2=4*2*(14+k)
easy to find k from here....

Answer 16

and wouldn't the vertex form be
(x-3)^2+5
and
-(x-10)^2-k+100

Answer 17

How can we set the equations to equal to eachother when they could be repersenting different parabolas that is what is confusing me

Answer 18

to find the points of intersection between any 2 curves y=f(x) and y=g(x), we solve them simultaneously, by letting f(x) = g(x), finding values of x and then y.

Answer 19

You are setting them equal for particular value of \(x\).