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{{ printedBook.courseTrack.name }} {{ printedBook.name }} To draw the graph of the given function, we will follow four steps.

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

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

Recall the factored form of a quadratic function. $y=a(x−p)(x−q) $ In this form, where $a$ $ =$ $0,$ the $x-$intercepts are $p$ and $q.$ Let's consider the factored form of our function. $f(x)=-2(x−3)(x+4)⇔f(x)=-2(x−3)(x−(-4)) $ We can see that $a=-2,$ $p=3,$ and $q=-4.$ Therefore, the $x-$intercepts occur at $(3,0)$ and $(-4,0).$

The axis of symmetry is halfway between $(p,0)$ and $(q,0).$ Since we know that $p=3$ and $q=-4,$ the axis of symmetry of our parabola is halfway between $(3,0)$ and $(-4,0).$ $x=2p+q ⇒x=23+(-4) =-21 $ We found that the axis of symmetry is the vertical line $x=-21 .$

$f(x)=-2(x−3)(x+4)$

Substitute$x=-21 $

$f(x)=-2(-21 −3)(-21 +4)$

Simplify right-hand side

WriteAsFracWrite as a fraction

$f(x)=-2(-21 −26 )(-21 +28 )$

AddSubFracAdd and subtract fractions

$f(x)=-2(-27 )(27 )$

MultNegNegOnePar$-a(-b)=a⋅b$

$f(x)=2(27 )(27 )$

DenomMultFracToNumber$2⋅2a =a$

$f(x)=7(27 )$

MoveLeftFacToNum$a⋅cb =ca⋅b $

$f(x)=249 $

Finally, we will draw the parabola through the vertex and the $x-$intercepts.