Question

If the quadratic function y=8x−4x2+5y=8x−4x2+5 is to be transformed in its vertex form, what number should be placed in the box?

Answer 1

Answer:

I can not see the image to see where is the box, so i will answer this in a more general way.

For a general quadratic equation:

y = f(x) = a*x^2 + b*x + c

The vertex form si:

y = a*(x - h)^2 + k

Where (h, k) is the vertex of our quadratic function.

such that h = -b/2*a

and k = f(h)

Then the first step here is to find the vertex of our quadratic function.

Our quadratic function is:

y = 8*x - 4*x^2 + 5

Let's rewrite this as:

y = f(x) =  -4*x^2 + 8*x + 5

then we have:

a = -4

b = 8

c = 5

Then here we have:

h = -b/(2*a) = -8/(2*-4) = -8/-8 = 1

h = 1

now to find the value of k we use:

k = f(1) = -4*1^2 + 8*1 + 5  = 9

Then we have:

h = 1

k = 9.

Then the vertex form of our function is:

y = -4*(x - 1)^2 + 9