To find the axis of symmetry and [tex]$y$[/tex]-intercept of the quadratic function [tex]\( f(x) = x^2 - 6x + 8 \)[/tex], we can follow these steps:
### Step 1: Determine the Axis of Symmetry
The standard form of a quadratic function is [tex]\( ax^2 + bx + c \)[/tex]. For the given function [tex]\( f(x) = x^2 - 6x + 8 \)[/tex], we have:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = -6 \)[/tex]
The formula for finding the axis of symmetry [tex]\( x \)[/tex] is:
[tex]\[ x = -\frac{b}{2a} \][/tex]
Substituting the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[ x = -\frac{-6}{2 \cdot 1} \][/tex]
[tex]\[ x = \frac{6}{2} \][/tex]
[tex]\[ x = 3 \][/tex]
Therefore, the axis of symmetry is:
[tex]\[ x = 3 \][/tex]
### Step 2: Find the Y-intercept
The [tex]\( y \)[/tex]-intercept of a function is the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex]. For the given function [tex]\( f(x) = x^2 - 6x + 8 \)[/tex]:
[tex]\[ f(0) = (0)^2 - 6(0) + 8 \][/tex]
[tex]\[ f(0) = 8 \][/tex]
Thus, the [tex]\( y \)[/tex]-intercept is:
[tex]\[ (0, 8) \][/tex]
### Summary
From the calculations above, we have determined:
- The axis of symmetry is [tex]\( x = 3 \)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\( (0, 8) \)[/tex].
So, the correct selections from the options provided are:
- [tex]\( x = 3 \)[/tex]
- [tex]\( (0, 8) \)[/tex]
