Determine the number of real solutions and complex solutions for each of the given graphs.
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For each of the following quadratic equations, a) Calculate the discriminant for the following quadratic equations,and then b) Use it to identify how many and what types of solutions exist.
4) \(0=5x^2-4x+1\)
5) \(0=\frac{1}{2}x^2+8x-5\)
6) \(0=9x^2-25\)
7) \(9x=\frac{1}{4}x^2\)
8) \(12x=4x^2+9\)
For problems 9-12, type a quadratic function in standard form into the Desmos applet with the given number and type of solutions. Write your function and explain why it works.
9) 2 real, irrational solutions 10) 2 complex solutions 11) 2 real, rational solutions 12) 1 real, rational solution |
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13) Without graphing, explain how you know that \(f(x)=-(x+4)^2+5\) has two real solutions.
14) Without graphing, explain how you know that \(f(x)=(x-2)^2+3\) has two complex solutions.
Review
15) Factor completely: \(-8x^2+4x+12\)
16) Solve by factoring: \(81x^2-64=0\)
17) Multiply: \((6-5i)(6+5i)\)
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