Identify the vertex for the graph of y = 3x² + 12x + 5.

Solution

The given equation is a quadratic equation of the form ax² + bx + c. 

Therefore a = 3;   b = 12 and c = 5.

Since a is +ve the parabola represented by this equation is opening upwards and the x - coordinate of its vertex is given by the expression

x = -b/2a

x = -12/2(3) = -2

The y- coordinate of the vertex can be obtained by substituting the value of x in the given quadratic equation :

y = 3x² + 12x + 5

  = 3(-2)²   + 12(-2) + 5

 = 3(4) - 24 + 5 

 = 12 - 24 + 5

 =  -7

The vertex of the graph of the equation is given by coordinates of (-2, -7)

Identify the vertex for the graph of y = 3x² + 12x + 5.

Summary:
The vertex for the graph of y = 3x² + 12x + 5 is the point with coordinates (-2, -7).