Write g(x) = –16x + x2 in vertex form. Write the function in standard form. Form a perfect square trinomial by adding and subtractingStartFraction b Over 2 EndFraction squared . Write the trinomial as a binomial squared. Write the function is in vertex form, if needed. G(x) = x2 – 16x b = –16, so StartFraction negative 16 Over 2 EndFraction squared = 64 g(x) = (x2 – 16x + 64) – 64 g(x) = (x – )2 –

Step-by-step explanation:

I'm not exactly sure what you're asking here, but I do know that to write a polynomial in vertex form you have to complete the square.

In standard form, our polynomial is

To put this into vertex form, set it equal to 0 first:

To complete the square, we need the leading coefficient to be a 1 and it is, so we're ready to begin the process of completing the square.

Take half the linear term, square it, then add it into both sides of the equation.  Our linear term is 16.  Half of 16 is 8, and 8 squared is 64 so we add 64 to both sides.

What we have accomplished by doing this is creating a perfect square binomial on the left which is

If we want to finish this off properly, we will move the 64 back over by the rest of the equation and set it back equal to y:

That's vertex form of the polynomial.

-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

34

step-by-step explanation: