Equation of Quadratic Function Given The Graphs and Zeros

• Quadratic function


  Function of the form y = ax^2 + bx + c
• Determining the equation of a quadratic function

  1. Given graph

  2. Given zeros (x-intercepts)

  3. Given vertex and a point
• The Wealth of Nations was written

  1776
• Rational (in classical economic theory)

  Economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Governments act rationally by


  Placing the interests of the people they serve first in order to maximise their welfare
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• Demand curve shifting right

  Increases the equilibrium price and quantity
• If you add up marginal utility for each unit you get total utility
• Vertex


  The point on the parabola where the graph changes from increasing to decreasing or vice versa
• Zeros

  The x-intercepts of the quadratic function
• Steps to determine the equation of a quadratic function

  1. Identify the vertex form: y = a(x-h)^2 + k

  2. Substitute the given vertex (h,k) and a point on the parabola to solve for a

  3. Substitute the values of a, h, and k into the vertex form to get the final equation
• Steps to determine the equation of a quadratic function from zeros

  1. Identify the zeros x1 and x2

  2. Write the equation in factored form: y = a(x-x1)(x-x2)

  3. Expand the factored form to get the standard form y = ax^2 + bx + c
• Quadratic functions can be represented graphically, algebraically, or through their zeros