Put these points in vertex form

Question

Put these points in vertex form 

(15,0) (25,32) (35,0)

Answer 1

Since the point (25, 0) lies halfway between the x-intercepts, (15,0) and (35,0), then by the symmetry of the parabola, the point (25, 32) must be the vertex.

 

So, the vertex form of the equation has the form y = A(x-25)² + 32

 

Since (15,0) is on the graph, we have 0 = 100A + 32

 

                                                       A = -32/100 = -8/25

 

Equation:  y = (-8/25)(x-25)² + 32

 

 

 

Answer 2

0 = a(15 - h)² + k

32 = a(25 - h)² + k

0 = a(35 - h)² + k

 

Three equations in three unknowns, solve the system.