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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-4)(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.

Answer :

frika

Answer:

A: x-intercepts: x = 4, x = 2,

y-intercept: y = 8

vertex: (3,-1)

axis of symmetry: x = 3

minimum: -1

B: See attached diagram

Step-by-step explanation:

Consider the function [tex]f(x) = x^2 - 6x +8.[/tex]

This function can also be represented in the following equivalent forms:

[tex]f(x) = (x-4)(x-2)\\ \\f(x) = (x - 3)^2 -1.[/tex]

Part A:

x-intecepts are the points where [tex]f(x)=0:[/tex]

[tex](x-4)(x-2)=0\\ \\x-4=0\ \text{or}\ x-2=0\\ \\x=4\ \text{or}\ x=2[/tex]

y-intercept is the point where [tex]x=0:[/tex]

[tex]f(x)=0^2-6\cdot 0+8=8[/tex]

The equation [tex]f(x)=(x-3)^2-1[/tex] is the equation of the parabola in vertex form, so the coordinates of the vertex are (3,-1)

Axis of symmetry is a vertical line which passes through the vertex. Hence, its equation is x = 3

Parabola opens upward, so it has minimum value and does not have maximum value.

Minumum value is at the vertex, so [tex]f_{min}=-1[/tex]

Part B:

Using the key features from Part A the graph of the function is as attached.

${teks-lihat-gambar} frika

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