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Core 1- Chapter 7 Question help ASAP!

Help me with this question please!

Find the value of the constant k so that the line y=2x+k is a tangent to the parabola with equation y=x^2-6x+2.

I presume it's something to do with the discriminant?

Reply 1

Tom777

Original post by TheDimpleboy

By definition a tangent intersects in exactly one place. You're right about the discriminant - you need to equate the equations and set the discriminant equal to 0.

Reply 2

TheDimpleboy

Original post by CJG21

Differentiate both functions, and find the value of x, and then y, when the functions have the same gradient.
Put these values into y=2x+k and you can find k.

Original post by Tom777

By definition a tangent intersects in exactly one place. You're right about the discriminant - you need to equate the equations and set the discriminant equal to 0.

I appreciate both your help but I'm still stuck, could either of you's please do a step by step instruction or post your working?

Reply 3

Tom777

Original post by TheDimpleboy

I appreciate both your help but I'm still stuck, could either of you's please do a step by step instruction or post your working?

You're not going to gain anything by letting other people do your work for you.

When you set two equations equal to each other you get a new equation in x. If you solve this equation you will find all values of x for which the two curves intersect.

You can then use the discriminant to find k such that the curves intersect in exactly one place - this is the definition of a tangent. To do this, set the discriminant equal to 0.

Summary:
Set equations equal to each other.
Set the discriminant equal to 0.
Solve for k.