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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

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Set y = 0 and solve for x:

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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.

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SOLUTION:

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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.

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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:

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Roots, Zeroes, and Solutions For Quadratics Day 2.

Roots, Zeroes, and Solutions For Quadratics Day 2.

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