The Vertex Point
Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 2 of 51.
The axis tells you where the vertex is from left to right. To finish the point, you need its height, and the height of any point on the curve is the function's output there. So the vertex is (h, f(h)): find h with -b/(2a), then evaluate f at h.
Take f(x) = 2x^2 + 8x + 1 again. Its axis is x = -2, so work out f(-2). Putting -2 into the rule gives 2(-2)^2 + 8(-2) + 1, which is 8 - 16 + 1, so the height is -7. The vertex is (-2, -7).
This gives you the vertex with no vertex form at all. It is also a check on later work: when you rewrite a parabola in vertex form, the point you read off must match the one this method gives.
Challenge
Last lesson you found the axis of f(x) = 3x^2 - 12x + 7: the line x = 2. Now find the height of its vertex. The board holds f(2). Tap Use f(x) = ..., then type the arithmetic line by line.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Quadratics & Complex Numbers
1The Vertex
The Axis of SymmetryThe Vertex PointMaximum or MinimumDrawing from Standard FormRecap: The Vertex2Completing 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 Parabolas