From Standard to Vertex
Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 12 of 51.
In Section 1 you read a parabola's vertex from vertex form, a(x - h)^2 + k. Completing the square is how you get there from standard form. The difference from solving is that an expression has no other side to add to, so you add the missing number and take it straight back off.
Take x^2 + 8x + 20. The missing number for x^2 + 8x is 16. Adding 16 and subtracting 16 changes nothing: x^2 + 8x + 16 - 16 + 20. The first three terms are (x + 4)^2, and -16 + 20 is 4, so the expression is (x + 4)^2 + 4.
Now the vertex can be read: (-4, 4). The square is never negative, so the smallest the expression can be is 4, reached at x = -4.
Challenge
Write x^2 - 6x + 11 in vertex form. Type each line: first the square with its borrowed number taken back, then the tidy form.
Try it yourself
Write it in vertex form
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Quadratics & Complex Numbers
2Completing the Square
Perfect Square TrinomialsThe Missing NumberCompleting the SquareIrrational AnswersWhen a Is Not 1Recap: Completing the Square5Complex Arithmetic
Adding and SubtractingMultiplyingThe ConjugateDividingA Pure Imaginary BottomRecap: Complex Arithmetic8Lines Meet Parabolas
Two CrossingsJust TouchingNo MeetingA Circle and a LineRecap: Lines and Parabolas3Vertex Form by Algebra
From Standard to VertexOdd Middle TermsA Leading NumberOpening DownRecap: Vertex Form