Question

question 10
which of the statements is false about the properties of quadratic function, ( f(x) = x^2 - 6x + 8 )?

• the axis of symmetry is ( x = 6 ).
• the y - intercept is ( (0, 8) ).
• the vertex is ( (3, -1) ).
• the parabola opens upward.

Explanation:

Step1: Find axis of symmetry

For $f(x)=ax^2+bx+c$, axis is $x=-\frac{b}{2a}$. Here $a=1, b=-6$:
$x=-\frac{-6}{2(1)}=3$

Step2: Calculate y-intercept

Set $x=0$: $f(0)=0^2-6(0)+8=8$, so intercept is $(0,8)$

Step3: Find vertex coordinates

Vertex x is axis of symmetry $x=3$. Compute $f(3)$:
$f(3)=3^2-6(3)+8=9-18+8=-1$, so vertex is $(3,-1)$

Step4: Check parabola direction

Since $a=1>0$, parabola opens upward.

Answer:

A. The axis of symmetry is x = 6.
B. The y-intercept is (0, 8).