Write the equation by using the x-intercepts. Don't forget you have a double root at x=-2 and a single root at x=2. Calculate the stretch factor by substituting any point from the graph into the formula.
y=- 1/4(x+2)(x+2)(x-2)
Practice makes perfect
Examining the coordinate plane, we notice that the graph has a double root at x=-2 and a single root at x=2.
Factored Form
If a polynomial has the roots x=a and x=b we can write its factors as follows.
&(x-a)
&(x-b)By substituting a=-2 and b=2 into the expressions above, we can determine the linear factors.
(x-(-2)) &⇔ (x+2)
(x-(2)) &⇔ (x-2)
Since the first root is a double root so we must include this factor twice. With this information, we can write the function in factored form.
y=k(x+2)(x+2)(x-2)
Stretch Factor
To determine the stretch factor k, we have to substitute a point that falls on the graph of the function into the equation and solve for k. We can pick any point we like except for the x-intercepts. Let us pick the y-intercept (0,2).
