Given the graph of the parabola shown below Write the equati

Given the graph of the parabola shown below. Write the equation of the parabola in vertex form, then expand it to write the equation in general form.

Solution

Vertex form of parabola is y=a(x-h)²+k where (h,k) is a vertex.

From the given graph, vertex=(h,k) =(4.10)and a point on parabola is (x,y) = (1,-17)

Substitute vertex and point in the vertex form of parabola.

y=a(x-h)²+k

-17 = a(1-4)² +10

-17 = a(-3)² +10

-17 = 9a+10

9a=-17-10

a=-27/9

a=-3

Therefore, vertex form of parabola is y=-3(x-1)²+10

General form is y=-3(x-1)²+10

     y=-3(x²+1²-2(x)(1))+10

    y=-3(x²+1-2x)+10

   y=-3x²-3+6x+10

  y=-3x²+6x+7

Therefore, general form is   y=-3x²+6x+7