IM Alg2.3.17 Lesson: Completing the Square and Complex Solutions

Match each equation in standard form to its factored form and its solutions.
What are the solutions to these equations?
[math](x-5)^2=0[/math]
[math](x-5)^2=1[/math]
[math](x-5)^2=\text{-}1[/math]
Solve these equations by completing the square.
[math]x^2-8x+13=0[/math]
[math]x^2-8x+19=0[/math]
[size=150]For which values of[math]a[/math] does the equation [math]x^2-8x+a=0[/math] have two real solutions? One real solution? No real solutions? Explain your reasoning.[/size]
How many real solutions does each equation have? How many non-real solutions?
[math]x^2-8x+13=0[/math]
[math]x^2-8x+16=0[/math]
[math]x^2-8x+19=0[/math]
How do the graphs of these functions help us answer the previous question?
[math]f(x)=x^2-8x+13[/math][br][math]g(x)=x^2-8x+16[/math][br][math]h(x)=x^2-8x+19[/math]
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