Question

Picture inside

Answer 1

@mathmale @mathstudent55 @alivejeremy

Answer 2

Have you heard about differentiation?

Answer 3

no

Answer 4

Okay then completing squares?

Answer 5

no

Answer 6

i have 2 common points and vertex below x-axis

Answer 7

y=-2x^2+x-3

Using completing squares.
.Take -2 out of brackets.
-2(x^2 -x/2 + 3/2)
then,
-2[(x-1/4)^2-(1/4)^2 + 3/2 ]
-2[(x-1/4)^2-1/16+3/2]
-2[(x-1/4)^2-23/16]
-2(x-1/4)^2-23/8

Answer 8

vertex is ( 1/4 , -23/8)

Answer 9

am i right?

Answer 10

There are no common points because b^2-4ac is < 0.
when the discriminant is <0 there are no common points ( 0 roots)
when its = 0 there is only one root e.g tangents to a curve
when its > 0 there is more than one root

y=ax^2+bx+c
in this case y=-2x^2+x-3
b is (1)x
a is (-2)x^2
c is (-3)

so b^2-4ac
1^2 - (4x-2x-3)
1-24 is 23 which is <0 there fore no roots hense no common points.

Answer 11

you sure?

Answer 12

Yeah.

Answer 13

where is the vertex?

Answer 14

under or below x-axis?

Answer 15

and i have another like this can you help?

Answer 16

it is below.. you have to study completing squares otherwise it will be really difficult.

Answer 17

thanks

Answer 18

can you help with another?

Answer 19

https://www.youtube.com/watch?v=xGOQYTo9AKY

check out this youtube video, im sure it'll help.

Answer 20

And this one also for discriminant

https://www.youtube.com/watch?v=lGZNaoHGsM8