Question

Find an equation for a line that is tangent to f(x)=x^2-2x-3

Answer 1

for any point? or do you want a formula for any point?

Answer 2

it doesn't specify, it just says to find an equation.

Answer 3

ok say we want to find the tangent line at x=a

Answer 4

f'(x)=2x-2

Answer 5

so the slope at x=a is f'(a)=2a-2

Answer 6

a line has the form y=mx+b

Answer 7

we know the slope m is 2a-2

Answer 8

so now we have y=(2a-2)x+b we now need to find the y-intercept

Answer 9

we know a point on this line (a,f(a))

Answer 10

f(a)=a^2-2(a)-3

Answer 11

a^2-2a-3=(2a-2)a+b

Answer 12

so we now solve this for b to find the y intercept

Answer 13

so we have y=(2a-2)x-a^2-3

Answer 14

this is the general equation for the tangent line at (a,f(a))

Answer 15

you think i can just pick a point off the original quadratic function and use those points, such as the point (3,0)?

Answer 16

It does say to find *an* so maybe it doesn't matter, but make sure the point is on the curve ( I mean verify that it is) Does f(3)=0?

Answer 17

since a point was not specified in the original problem and yes, f(3)=0.

Answer 18

ok you can use this point as long as we aren't looking for anything general.

Answer 19

ok thanks so much, i don't need to find the x and y intercepts right?

Answer 20

no. you can just use the general tangent line that I came up with. lol

Answer 21

but your teacher will probably want you to show work

Answer 22

ok thanks so much for your help :)