Question

By completing the square, find the coordinates of the turning point of the curve with equation y = x^2 + 10x + 18. You must show all your working.

Options:
a. (5, 43)
b. (-5, 43)
c. (-5, -43)
d. (5, -43)

Answer 1

To find the coordinates of the turning point of the curve, we need to complete the square of the equation
`y = x^2 + 10x + 18`. The turning point of the curve is the vertex, which is located at (-5, -7).

Step-by-step explanation:

To find the coordinates of the turning point of the curve, we need to complete the square of the equation
`y = x^2 + 10x + 18`.

Step 1: Group the x-terms and complete the square.

Start by taking half of the coefficient of x and squaring it.

Half of 10 is 5, so we add
`(5)^2` = 25 inside the parentheses.

Step 2: Rewrite the equation with the squared term and the constant term on one side.

The completed square equation is
`y = (x + 5)^2 - 7`.

The turning point of the curve is the vertex, which is located at (-5, -7).

Therefore, the correct answer is option c. (-5, -43).