What is the vertex of the graph of the function below?
y= x2 - 8x+ 12
o a. (2,0)
o b. (4,0)
o c. (2,-4)
o d. (4,-4)

D. (4, -4)

Step-by-step explanation:

Convert to vertex form by completing the square.

For a polynomial y = x² + bx + c, first add and subtract (b/2)² to the polynomial.  Then factor.

Here, b = -8.  So (b/2)² = (-8/2)² = 16.

y = x² − 8x + 12

y = x²− 8x + 16 − 16 + 12

y = (x − 4)² − 16 + 12

y = (x − 4)² − 4

The vertex is (4, -4).

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)