The standard form of the equation of a parabola is y = 5x2 + 20x + 14. What is the vertex form of the equation?

The vertex form of quadratic equation is expressed as:

y = a (x - h) ² + k

We manipulate the given equation to be the same as the vertex form. First we transpose the constants to the left-hand side.

y - 14 = 5x² + 20x

Then, we factor out in right hand side the coefficient of the x² term.

y - 14 = 5 (x² + 4x)

We divide the coefficient of the x term with 2 and take its square. We add this value to both sides of the equation but we should remember that in the left-hand side we should multiply this value with five to keep it balanced.

y - 14 + 20 = 5 (x² + 4x + 4)

We simplify the right-hand side as:

y + 6 = 5 (x + 2) ²

We can now manipulate further the equation above in the vertex form. Thus,

y = 5 [ x - (-2) ]² - 6