Graph the function f(x)= -(x-2)^2 +4. In what form is this quadratic function written? . List the values of the following parameters:a = h = k = Vertex =

see below

Step-by-step explanation:

f(x)= -(x-2)^2 +4

This is the vertex form of the equation for a parabola

y= a ( x-h)^2 +k  where (x,k) is the vertex of the parabola

a = -1   h= 2   k = 4

The vertex is ( 2,4)

Completed square form

a = -1

h = 2

k = 4

Vertex: (2,4)

Step-by-step explanation:

f(x)= -(x-2)^2 +4 is in the complete square form

f(x) = a(x - h)² + k

a = -1

h = 2

k = 4

Vertex: (2,4)

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.