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Consider the function f(x) = x2 - 6x +8.

This function can also be represented in the following equivalent forms:
f(x) = (x - 1)(x - 2)
f(x) = (x – 3)2 -1.
Part A: Identify the following key features from the
different forms of the function.
X-intercept(s):
y-intercept:
vertex:
axis of symmetry:
max/min value:
Part B: Use the key features from Part B to graph
the function f(x) = x2 - 6x +8.

Respuesta :

Answer:

A function that has an axis of symmetry at x = 3 is:

f (x) = x ^ 2 - 6x - 1

Step-by-step explanation:

A parabola has an axis of symmetry at x = 3 if the x-value of the vertex is 3.

f(x) = x^2 + 3x + 1 = x^2 + 3x + 9/4 - 5/4 = (x + 3/2)^2 - 5/4 => vertex = (-3/2, -5/4)

f(x) = x^2 - 3x - 3 = x^2 - 3x + 9/4 - 21/4 = (x - 3/2)^2 - 21/4 => vertex = (3/2, -21/4)

f(x) = x^2 + 6x + 3 = x^2 + 6x + 9 - 6 = (x + 3)^2 - 6 => vertex = (-3, -6)

f(x) = x^2 - 6x - 1 = x^2 - 6x + 9 - 10 = (x - 3)^2 - 10 => vertex = (3, -10)

Therefore, f(x) = x^2 - 6x - 1 has an axis of symmetry at x = 3.

Hope This HELPS!!!

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