The function h(x)=x^2+3and g(x)=x^2-6. if g(x)=h(x)+k, what is the value of k

The value of k is - 9

Step-by-step explanation:

∵ h(x) = x² + 3

∵ g(x) = x² - 6

∵ g(x) = h(x) + k

- To find the value of k substitute g(x) by x² - 6 and h(x) by x² + 3

   in the equation above to find k

∵ x² - 6 = x² + 3 + k

- Subtract 3 from both sides

∴ x² - 6 - 3 = x² + 3 + k - 3

- Add the like terms in both sides

∴ x² - 9 = x² + k

- Subtract x² from both sides

∴ - 9 = k

∴ The value of k is - 9

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3