SOLUTION: It is given that the axis of symmetry of the graph of the function y=x^2+kx+5＝-3. Find the value of k.

Algebra ->  Functions -> SOLUTION: It is given that the axis of symmetry of the graph of the function y=x^2+kx+5＝-3. Find the value of k.      Log On


   

Question 1005900: It is given that the axis of symmetry of the graph of the function y=x^2+kx+5＝-3. Find the value of k.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given that the axis of symmetry of the graph of the function y=x%5E2%2Bkx%2B5=-3. Find the value of k.
recall: The axis of symmetry of a parabola is the vertical line through the vertex. For a parabola in standard form, y+=+ax%5E2+%2B+bx+%2B+c, the axis of symmetry has the equation x=+-b%2F2a.
Note that -b%2F2a is also the x-coordinate of the vertex of the parabola.
if x%5E2%2Bkx%2B5=-3, where a=1 and b=k we have
x=+-k%2F2%2A1
x=+-k%2F2
2x=+-k
k=-2x....substitute in given equation and solve for x

x%5E2-2x%2Ax%2B5=-3
x%5E2-2x%5E2%2B5=-3
-x%5E2%2B5=-3
3%2B5=x%5E2
8=x%5E2
x=sqrt%288%29
x=2sqrt%282%29
or x=-2sqrt%282%29
then, go back to k=-2x, substitute values 2sqrt%282%29 and -2sqrt%282%29 for x and find k

k=-2x=>k=-2%2A2sqrt%282%29=>k=-4sqrt%282%29
or
k=-2x=>k=+-2%2A%28-2sqrt%282%29%29=>k=4sqrt%282%29
so, your equations are:
y=x%5E2-4sqrt%282%29x%2B5 or y=x%5E2%2B4sqrt%282%29x%2B5