Write each function in the form fxaxh2k then find each of th

Write each function in the form f(x)=a(x-h)^2+k; then find each of the following algebraically without using any graphs:

A). Intercepts B). Vertex C). Maximum or minimum D). Range

N(x)=-10+8x-x^2

Solution

N(x)=-10 +8x-x²

N(x)=-(x²-8x)-10

N(x)=-(x²-8x +16-16)-10

N(x)=-(x-4)²+6

To find the y intercept we have to plug x=0

N(x)=-(0-4)²+6=-10

Hence the y intercept is (0,-10)

To find the x intercept we have to plug N(x)=0

0=-(x-4)²+6

x=1.551,6.449

Therefore x intercept is (1.551,0),(6.449,0)

B. vertex

This is of the form y=a(x-h)²+k

Where (h,k) is the vertex which is (4,6) here

C. Maximum or minimum

Maximum at its vertex that is at (4,6)

D. As we see here that the graph is maximum at y=6. Therefore y cant take values greater than 6

Hence range=(-infinity,6]