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Mathematics · Grade 9

Quadratic Functions and Equations

Learners read the vertex, axis of symmetry, intercepts and direction of a parabola from its standard, vertex and factored forms, then solve quadratic equations by factoring, square roots, completing the square and the quadratic formula, using the discriminant to predict the number of real solutions. Projectile and area models end the course, with attention to rejecting solutions that make no sense. An optional honors lesson derives the quadratic formula.

  • 5 lessons
  • About 140 minutes
  • Quadratics check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, plot points, match pairs, type a number and place on a number line
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What learners will discover

  • Identify the vertex, axis of symmetry, intercepts and direction of opening of a parabola, and explain which features standard, vertex and factored forms reveal.
  • Solve quadratic equations by factoring (using the zero product property) and by taking square roots.
  • Solve quadratic equations by completing the square and with the quadratic formula, and use the discriminant to determine the number of real solutions.
  • Model projectile and area situations with quadratic functions and interpret solutions, maxima and minima in context, rejecting impossible solutions.

Lessons

  1. Graphs and forms of quadratic functions 7 steps5 practiceabout 30 min
  2. Solving by factoring and square roots 7 steps4 practiceabout 28 min
  3. Completing the square, the formula and the discriminant 6 steps4 practiceabout 32 min
  4. Quadratic models 7 steps5 practiceabout 30 min
  5. Going further (honors): deriving the quadratic formula 4 steps1 practiceabout 20 min
  6. Quadratics check 11 questions at the end

Keep exploring

More 9th grade math

Guide for grown-ups