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,
Option B is the correct answer because you start with 15 gallons (y-intercept), and the car consumes or decreases at 0.03 gal/per mile (your slope or m).
