 Understand that the x-intercepts of a quadratic relation are the solutions to the quadratic equation  Factor a quadratic relation and find its x- intercepts, and then sketch the graph  Solve real-world problems by factoring a quadratic equation and finding the intercepts of the corresponding quadratic relation   Determine the equation of a quadratic relation in the form y = a(x – r)(x – s) from a graph

 Set y = 0 and solve for x:

 The x-intercepts(or zeros) of the quadratic relation  are the solutions to the quadratic equation  If the x-intercepts r and s are found, the x- coordinate of the vertex is  The y-coordinate of the vertex is found by substituting the x-coordinate into the original equation.

 SOLUTION:

 1) Two x-intercepts – two different factors leads to two solutions – graph crosses twice.  2) One x-intercept – factor is a perfect square that leads to one solution – graph just touches the x-axis.  3) No x-intercepts – cannot solve the quadratic equation by factoring – graph never touches the x-axis.

 An engineer uses the equation  to design an arch, where h is the height in metres and d is the horizontal distance in metres. How wide and tall is the arch?  Solution: