What are the zeros, axis of symmetry and vertex of each equation

Question

A) y=3x^2+15x+18

b) y=-2x^2+4x+6

Answer 1

We can find the zeros, axis of symmetry, and vertex by putting the functions in vertex form.

 

y = a(x - h)² + k

 

where:

a is the coefficient of x² term

vertex has coordinates (h, k)

 

 

A)

 

y = 3x² + 15x + 18

 

 

in vertex form,

 

y = 3(x² + 5x + (25/4)) - (3/4)              the term in bold parenthesis is the squared term.

 

y = 3(x + 5/2)(x + 5/2) - (3/4)

 

y = 3(x + 5/2)² - 3/4

 

 

The axis of symmetry is the x coordinate of the vertex.  

Vertex is (-5/2, -3/4)

The axis of symmetry is  x=-5/2

 

 

To find the zeros, set y=0.  Use the vertex form of the function.

 

0 = 3(x + 5/2)² - 3/4

 

 

Solve for x.

 

3/4 = 3(x + 5/2)²

 

1/4 = (x + 5/2)²

 

±√(1/4) = x + 5/2

 

± 1/2 = x + 5/2

 

-5/2 ± 1/2 = x

 

 

-5/2 + 1/2 = x                 and                     -5/2 - 1/2 = x

 

-4/2 = x                          and                      -6/2 = x

 

-2 = x                              and                         -3 = x

 

 

Now that you understand the procedure, try the other problem on your own.