The equation of a curve is y = 4x^2 - 56x The curve has one turning point - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 3

To find the turning point of the curve, we first need to rewrite the equation in completed square form.

Starting with:

$y = 4x^2 - 56x$

We can factor out 4 from the first two terms:

$y = 4(x^2 - 14x)$

Next, we complete the square inside the parentheses. To do this, we take half of the coefficient of x (which is -14), square it, and add and subtract it inside the parentheses:

Half of -14 is -7, and squaring that gives us 49. Thus, we write:

$y = 4(x^2 - 14x + 49 - 49)$

Which simplifies to:

$y = 4((x - 7)^2 - 49)$

Distributing the 4 gives:

$y = 4(x - 7)^2 - 196$

From this form, we can identify the vertex of the parabola, which represents the turning point. The vertex is at (h, k) where the equation is in the format ( y = a(x - h)^2 + k ).

Thus, the turning point of the curve is at (7, -196), confirming our goal.