Vertex form is y = a(x - h)^2 + k. How do you write the quadratic function y = -3x^2 + 18x + 7 in vertex form?

Question

y = 3(x - 3)^2 + 34

y = -3(x + 3)^2 + 7

y = 18(x - 3)^2 + 7

y = -3(x - 3)^2 + 34

y = -3(x + 3)^2 - 74

Answer 1

You can put the equation in the form y = a(x-h)²+k by completing the square.

 

y = -3x²+18x+7

 

   = -3(x²-6x)+7

 

   = -3(x²-6x+9-9)+7  {the number 9 is obtained by taking half of -6                                         and squaring that number} 

 

   = -3(x-3)² + 27 + 7

 

y = -3(x-3)²+34

 

So, the vertex (highest point on the parabola) is (3,34).