The equation of a curve is y = 4x^2 − 56x

The equation of a curve is y = 4x^2 − 56x. The curve has one turning point. By completing the square, show that the coordinates of the turning point are (7, −196) You must show all your working. 

The given equation of the curve is y = 4x^2 − 56x. To find the turning point of the curve, we need to complete the square. First, let’s rewrite the equation in the form y = a(x – h)^2 + k, where (h, k) represents the coordinates of the turning point. 

To complete the square, we need to factor out the coefficient of x^2, which is 4 in this case. This gives us y = 4(x^2 – 14x). Now, we need to add and subtract (14/2)^2 = 49 inside the parentheses to complete the square. This gives us y = 4(x^2 – 14x + 49 – 49). 

Simplifying further, we get y = 4((x – 7)^2 – 49). Finally, expanding the equation gives us y = 4(x – 7)^2 – 196. Therefore, the coordinates of the turning point are (7, -196) as shown by completing the square of the given equation.

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