Answer:
y = a · (x -(h +√(-k/a))) · (x -(h -√(-k/a))) . . . . . . from y = a(x -h)² +k
Explanation:
You want to know how to write an equation in intercept form from vertex form.
Solve for x
"Intercept form" of the equation of a parabola is the factored form. The x-intercepts are the values of x that make the factors zero. This form can be found from vertex for by solving for the x-intercepts—the values of x where y=0.
X-intercepts
The vertex form equation is ...
y = a(x -h)² +k . . . . . . . vertex (h, k)
Solving for x when y=0, we have ...
0 = a(x -h)² +k
-k/a = (x -h)² . . . . . . . subtract k and divide by 'a'
±√(-k/a) = x -h . . . . . take the square root
x = h ±√(-k/a) . . . . . add h
These are the x-intercepts.
Intercept form
To write the equation in intercept form, we use these values to form factors of the quadratic. Each x-intercept (p) corresponds to a factor (x-p). The factors are multiplied by 'a' to keep the same vertical scaling of the graph that the original function had.
y = a · (x -(h +√(-k/a))) · (x -(h -√(-k/a))) . . . . . . intercept form