What is the function f(x)=3(x^2-8x)+10 written in vertex form

y = 3(x - 4)² - 38

Step-by-step explanation:

We need to complete the square on

   y = 3(x² - 8x) + 10

A quadratic equation is in the form of y = ax² + bx + c.  To complete the square, take half of the b term (here, the b term is -8), then square it...

-8/2 = -4

(-4)² = 16

Now add and subtract that from the equation...

y = 3(x² - 8x + 16 - 16) + 10

Now pull out the -16 from the parenthesis, be careful though, there is a  multiplier of 3 in front of the parenthesis, so it come out as a positive -48

y = 3(x² - 8x + 16) + 10 - 48

x² - 8x + 16 is a perfect square trinomial (we did this by completing the square), so it factors to (x - 4)², and 10 - 48 = -38, so our equation becomes...

y = 3(x - 4)² - 38

This is now in vertex form, which is either the minimum or maximum.

Vertex form is

y = a(x - h)² + k, where (h, k) is the vertex.  If a > 0, then the vertex is a minimum, if a < 0, then the vertex is a maximum.

Our vertex is (4, -38)

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.

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