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Unit 4 · 5 lessons

Quadratic Relations

Meet the parabola: recognize quadratic relations from data, tables and equations, read the vertex, axis, zeros and maximum or minimum, graph y = a(x − h)² + k by transforming y = x², use factored form and completing the square, and compare y = x² with y = 2ˣ to make sense of zero and negative exponents.

  • 57 practice questions
  • 41 flashcards
  • 4 interactive lessons
Start lesson 1 →Unit 4 test review →

Lessons

  1. 1Quadratic Relations and Their PropertiesA quadratic relation has a U-shaped graph called a parabola, and a table of values whose second differences are constant. Learn to recognize one from data, a table or an equation, and to name its key features: the vertex, the axis of symmetry, the zeros, the y-intercept and the maximum or minimum value.11 questions
  2. 2Transformations and Vertex FormEvery parabola in this course is a copy of y = x² that may be stretched or compressed, flipped, and slid to a new position. Learn what a, h and k do in y = a(x − h)² + k, sketch a parabola by hand from its vertex, and find the equation of a parabola from its graph.Interactive11 questions
  3. 3Factored Form and ZerosWhen a quadratic is written as a product, y = a(x − r)(x − s), its zeros are r and s, the axis of symmetry is halfway between them, and the vertex is one substitution away. Connect factoring from the last unit to the x-intercepts of a graph, sketch parabolas from their zeros, and build an equation from its zeros and one point.Interactive12 questions
  4. 4Completing the SquareCompleting the square rewrites y = ax² + bx + c in vertex form, y = a(x − h)² + k, so the vertex and the maximum or minimum value can be read directly. Build the idea with algebra tiles, follow the steps with and without a leading coefficient, and choose the best way to graph any quadratic: factoring, completing the square, partial factoring or technology.Interactive11 questions
  5. 5Comparing y = x squared and y = 2 to the xThe relations y = x² and y = 2ˣ look alike for small x, but one is a parabola and the other doubles at every step. Compare their tables and graphs, see why 2ˣ eventually overtakes x² for good, and use the pattern in the table of y = 2ˣ and the exponent laws to give meaning to zero and negative exponents.Interactive12 questions