To draw the graph of the given function, we will follow four steps.
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.
Finally, we will draw the parabola through the vertex and the x-intercepts.