3. Given vertex: (4,0), going through the point (3, 1), write the vertex form equation.

Step-by-step explanation:

The vertex form of an equation of the parabola:  

                                                         f(x) = a(x - h)² + k

the vertex is (4, 0)  ⇒   h = 4,  k = 0

so:

      f(x) = a(x - 4)² + 0

      f(x) = a(x - 4)²

The parabola goes through the point (3, 1) ⇒   x=3,  f(x)=1

1 = a(3 - 4)²

1 = a(-1)²

1  = a

It means the equation of the parabola in vertex form:

                                f(x) = (x - 4)²

2

step-by-step explanation: