Question

Please help!!

Find the coordinates of the vertex of the following parabola algebraically. Write your
answer as an (x, y) point.
y = 4x + 56x + 192

Answer 1

The vertex of the parabola = (-7 , -4)

Explanation:

Step(i):-

Given that the parabola y = 4 x² + 56 x +192

y = 4 (x² + 14 x + 48 )

y = 4 ( x² + 2 × 7 (x) + 49-1)

y = 4 ( x² + 2 × 7 (x) + 49)- 4

we apply the formula

(a +b)² = a² + 2ab + b²

y = 4 ( x + 7 )² - 4

Step(ii):-

The general form of the parabola in algebraically

y = a ( x-h)² +k

The equation

y = 4 ( x + 7 )² - 4

y = 4 ( x-(-7))² - 4

The vertex of the parabola (h,k) = (-7 , -4)

Final answer:-

The vertex of the parabola = (-7 , -4)