Write the quadratic function in the form fxaxh2 k fx 3x224x

Write the quadratic function in the form f(x)=a(x-h)^2 + k

f(x)= -3x^2+24x-46

Solution

f(x)= -3x^2 + 24x - 46

we have to make this equation in the form f(x) = a(x - h)^2 + k

we can see that there is a perfect square \"(x-h)^2 \"

so we have to make the x-terms a perfect square

f(x)= -3x^2 + 24x - 46
f(x) = -3 (x^2 -8x) -46    we have plug out \"-3\" as GCF from (-3x^2 +24x)

now we have to make (x^2 -8x) as perfect square

we divide the coefficient of x-term by \"2\" and then square the result obtained

here coefficient of x term is 8.

we divide it by \"2\" we get \"4\"

now we square it we get \"16\"

now we add and subtract this number \"16\" inside the bracket

f(x) = -3 (x^2 - 8x + 16 -16 ) - 46     

f(x) = -3 (x^2 -8x +16 ) +48 - 46 (we move out \"-16\" outside the bracket since \"-3\" is multipled so we get -16*-3 =48 )

f(x) = -3 (x-4)^2 + 2

now it is in the form f(x)=a(x-h)^2 + k

here \"(h,k)\" is the vertex of the graph

on comparing

f(x) = -3 (x-4)^2 + 2

f(x) = a (x-h)^2 + k

we get h=4 and k=2

so the vertex is (4,2)