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. f(x)=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)=(x−2)(x+2)⇔f(x)=1(x−2)(x−(-2))
We can see that a=1, p=2, and q=-2. Therefore, the x-intercepts occur at (2,0) and (-2,0).
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p=2 and q=-2, the axis of symmetry of our parabola is halfway between (2,0) and (-2,0). x=2p+q⇒x=22+(-2)=20=0 We found that the axis of symmetry is the vertical line x=0.
Finally, we will draw the parabola through the vertex and the x-intercepts.