# graph the function and state the vertex, the axis of symmetry, the intercept f(X)=X^2-6X+8MUST SHOW WORK

lfryerda | High School Teacher | (Level 2) Educator

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To find the y-intercept of any function, we set x=0 and solve for y.  That means that

`f(0)=0^2-6(0)+8=8`

so the y-intercept is y=8, or (0,8).

To find the x-intercept, we set y=0 and solve for x.  With quadratics, it is easiest to factor the quadratic and set each factor to zero.

This means

`f(x)=x^2-6x+8`

`=(x-2)(x-4)`

`f(x)=0`  at `(x-2)(x-4)=0`

so the x-intercepts are at x=2 and x=4.

The axis of symmetry is the x-value that is half way between the x-intercepts.

This is at `x={2+4}/2=6/2=3`.

The vertex is the point where the function is evaluated at the axis of symmetry.

The vertex is at

`f(3)=(3-2)(3-4)=(1)(-1)=-1`

which is the point (3,-1).

The graph is then the parabola that goes through these points.

The y-intercept is (0,8), the x-intercepts are (2,0) and (4,0), the axis of symmetry is x=3 and the vertex is (3,-1).