Question

1. $f(x) = -(x - 4)(x - 2)$

Explanation:

Step1: Find x-intercepts

Set $f(x)=0$:
$-(x-4)(x-2)=0$
Solutions: $x=4$ and $x=2$, so intercepts at $(4,0)$ and $(2,0)$.

Step2: Find vertex (midpoint of roots)

x-coordinate: $\frac{2+4}{2}=3$
Substitute $x=3$ into $f(x)$:
$f(3)=-(3-4)(3-2)=-(-1)(1)=1$
Vertex at $(3,1)$.

Step3: Find y-intercept

Set $x=0$:
$f(0)=-(0-4)(0-2)=-(-4)(-2)=-8$
Y-intercept at $(0,-8)$.

Step4: Determine parabola direction

The coefficient of $x^2$ (expand to check: $f(x)=-(x^2-6x+8)=-x^2+6x-8$) is $-1<0$, so parabola opens downward.

Answer:

To graph $f(x)=-(x-4)(x-2)$:

1. Plot x-intercepts at $(2, 0)$ and $(4, 0)$
2. Plot vertex at $(3, 1)$
3. Plot y-intercept at $(0, -8)$
4. Draw a downward-opening parabola passing through all these points, symmetric about the vertical line $x=3$.