Find the value of c such that the line with equation y= 2x + c is a tangent to the parabola y = x squared + 3x

c=-1/4

Step-by-step explanation:

Y=2x+c=2(x+c/2), so m=2.

To be tangent we need to check y’ of parabola: y’=2x+3.

So for some x it must be 2x+3=2 (cause m=2). We have x=-1/2.

Now we use x=-1/2 to find y from 2nd equation (equation of parabole): we got y=1/4-3/2=-5/4.

So tangent has point (-1/2,-5/4).

Put that point in firts equation (equation of line): -5/4=-1+c,

so we have c=-1/4.

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answer4 to the second power is 16

and 4 to the third power is 64,