Complete the square to find a maximum or minimum value
Complete the square to convert a quadratic to vertex form and find its maximum or minimum value, including a fencing-optimization word problem. Unlimited questions, five difficulty levels, and a full worked solution every time, included free with weekly lessons.
Try one
Complete the square to find the minimum value of the function.
y = 2x2 - 8x + 6
Answer: -2
See one solved, step by step
Complete the square to find the minimum value of the function.
y = 2x2 + 12x + 20
📘 Worked solution
1y = 2x2 + 12x + 20Start with the quadratic in standard form.
2y = 2(x2 + 6x) + 20Factor 2 out of the first two terms.
3y = 2(x + 3)2 + 20 - 18Add and subtract (6/2)^2 = 9 inside the brackets to make a perfect square, compensating outside.
4y = 2(x + 3)2 + 2Combine the constants: 20 and -18 add to 2. This is vertex form.
5The minimum value is 2, at x = −3.a = 2 > 0, so the parabola opens upward and the vertex is the lowest point.
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