To draw the graph of the given function, we will follow four steps.

- Identify and plot the .
- Find and graph the .
- Find and plot the .
- Draw the through the vertex and the points where the $x-$intercepts occur.

Let's go through these steps one at a time.

### Identify and Plot the $x-$intercepts

Let's start by recalling the of a .
$f(x)=a(x−p)(x−q) $
In this form, where $a$ $ =$ $0,$ the $x-$intercepts are $p$ and $q.$ Let's consider the given function.
$f(x)=-4(x−7)(x−3) $

We can see that $a=-4,$ $p=7,$ and $q=3.$ Therefore, the $x-$intercepts occur at $(7,0)$ and $(3,0).$

### Find and Graph the Axis of Symmetry

The axis of symmetry is halfway between $(p,0)$ and $(q,0).$ Since we know that $p=7$ and $q=3,$ the axis of symmetry of our parabola is halfway between $(7,0)$ and $(3,0).$
$x=2p+q ⇒x=27+3 =210 =5 $
We found that the axis of symmetry is the $x=5.$

### Find and Plot the Vertex

Since the vertex lies on the axis of symmetry, its

$x-$coordinate is

$5.$ To find the

$y-$coordinate, we will substitute

$5$ for

$x$ in the given equation.

$f(x)=-4(x−7)(x−3)$

$f(5)=-4(5−7)(5−3)$

$f(5)=-4(-2)(2)$

$f(5)=8(2)$

$f(5)=16$

The

$y-$coordinate of the vertex is

$16.$ Therefore, the vertex is the point

$(5,16).$
### Draw the Parabola

Finally, we will draw the parabola as a curve passing through the vertex and the $x-$intercepts.