Question

The line y = 2x + 3 is tangent to the parabola y = x2 + B. Find B.

Can someone explain this step by step

Answer 1

so y=x^2+B
=> y'=2x+0
=>y'=2x


The slope of the tangent line is 2

so 2x=2
=> x=1
=>y=2(1)+3=5
=>5=1^2+B
=>5-1=B
=>B=4

Answer 2

ahhh makes sense now

Answer 3

awesome! :)

Answer 4

I just dont get why you plug that x back into the tangent line equation then set the it equal to the b equation

Answer 5

I'm trying to the connect the relationship but idk

Answer 6

ok well i know that (x,y) is on both y=x^2+B and y=2x+3

Answer 7

well the point that they touch I'm calling (x,y)

Answer 8

we knew x

Answer 9

from setting the derivative=slope of the tangent line and solving for x

Answer 10

so i had enough info to find out what y was on y=2x+3

Answer 11

which would also be the same y on y=x^2+B

Answer 12

AH thats right the derivative of that equation is the slope at that point?

Answer 13

Yep! :)

Answer 14

SWEET thank you! I wish I could give you two medals for this lol!

Answer 15

i give medal too -- theres your second medal! :D

Answer 16

I don't need medals. I just need your love (platonic love of course). :)

Answer 17

Thanks you guys. You are so sweet.

Answer 18

You has my math thats more than my love.