Maximum/minimum of a quadratic by completing the square
Complete the square to find the maximum or minimum value of a quadratic function. 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 = x2 + 8x + 18
Answer: 2
See one solved, step by step
Complete the square to find the minimum value of the function.
y = x2 - 4x + 3
📘 Worked solution
1y = x2 - 4x + 3Start with the quadratic in standard form.
2y = 1(x2 - 4x) + 3Factor 1 out of the first two terms.
3y = 1(x - 2)2 + 3 - 4Add and subtract (-4/2)^2 = 4 inside the brackets to make a perfect square, compensating outside.
4y = 1(x - 2)2 - 1Combine the constants: 3 - 4 = -1. This is vertex form.
5The minimum value is −1, at x = 2.a = 1 > 0, so the parabola opens upward and the vertex is the lowest point.
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