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

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

A.  y = -3(x + 3)^2 - 74
B.  y = 18(x - 3)^2 + 7
C.  y = -3(x + 3)^2 + 7
D.  y = 3(x - 3)^2 + 34
E.  y = -3(x - 3)^2 + 34

Answer 1

The x component of the vertex is determined by the formula -b/2a given a quadratic ax² + bx + c.

The y component of the vertex is determined by solving the quadratic for y using the x component derived above.

 

x component of vertex = -18         -18

                                   -------  = ------ = 3

                                   (2)(-3)       -6

 

Use x=3 in the original quadratic to solve for y

y = -3(3)² + 18(3) + 7 

y = -27 + 54 + 7

y = 34

 

So the vertex point is (3,34)

 

And the vertex form of the equation is y = -3(x-3)² + 34

Notice the x² coefficient from the original equation is used in the vertex form as well.

 

The answer is E.

Answer 2

To put the given equation in the form y = a(x-h)²+k, complete the square:

 

y = -3x² + 18x + 7

 

   = -3(x² - 6x) + 7

 

   = -3(x² - 6x + 9 - 9) + 7

 

   = -3(x² - 6x + 9) + 27 + 7

 

y = -3(x-3)² + 34

 

So the vertex is (3,34).