Now that we have the standard form of the function, we can write it in intercept form by factoring out the greatest common factor 2x.
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Standard Form & &Intercept Form [0.5em]
g(x)=2x^2-4x & ⇔ & g(x)=2x(x-2)
b To draw the graph of the given function, we will follow four steps.
Draw the parabola 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
Recall the intercept form of a quadratic function.
g(x)=a(x-p)(x-q)
In this form, where a ≠0, the x-intercepts are p and q. Let's consider the intercept form of our function.
g(x)=2x(x-2)
⇕
g(x)= 2(x- 0)(x- 2)
We can see that a= 2, p= 0, and q= 2. Therefore, the x-intercepts occur at ( 0,0) and ( 2,0).
Find and Graph the Axis of Symmetry
The axis of symmetry is halfway between (p,0) and (q,0). Since we know that p=0 and q=2, the axis of symmetry of our parabola is halfway between (0,0) and (2,0).
x=p+q/2 ⇒ x=0+ 2/2=2/2=1
We found that the axis of symmetry is the vertical line x=1.
Find and Plot the Vertex
Since the vertex lies on the axis of symmetry, its x-coordinate is 1. To find the y-coordinate, we will substitute 1 for x in the given equation.
