[Precalculus] Rewrite equation from quadratic form to shifted form

Question

Given the quadratic equation y = 3x2 + 18x + 1

a.) Write the quadratic in shifted form (i.e. y = a(x−h)2 + k)

 

 

Answer 1

y = 3x² + 18x + 1

 

y = 3(x² + 6x + 9) + 1 - 27

y= 3(x + 3)² - 26

Answer 2

A quadratic function in shift form (aka vertex form) has these values:

 

a = the coefficient of x²

(h, k)= vertex of the parabola

 

 

Looking at our function, we will have

 

y = 3(x² + 6x + 9) - 26

 

y = 3(x + 3)(x + 3) - 26

 

y = 3(x + 3)² - 26