Question

Express y = 2x^2 + 4x + 17 in the form y = a(x + b)^2 + c, where a, b and c are constants. Hence, state the minimum value of y and the value of x at which this occurs. Sketch the curve y = 2x^2 + 4x + 17.

Answer 1

Your first need to complete the square. This gives you
y = 2(x + 1)^2 + 15

From here you can find the minimum value; x = -1 and you can figure out what y is. Then sketch the parabola.