5.2- solving quadratics, radicals, and i - weebly
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5.2 Solving, Radicals & i (Miller).notebook
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November 09, 2020
5.2- Solving Quadratics, Radicals, and iEssential Question: What are different ways we can solve quadratic functions?
Solutions are the same thing as ________, ________, & _____________!
Example 1: Solve each by graphinga) x2 x 6 = 0 b) 2x2 2 = 4x
Example 2: Solve each equation using square roots.
a) 4x2 31= 49
5.2 Solving, Radicals & i (Miller).notebook
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Example 2: Solve each equation using square roots.
b) 3x2 + 9 = 0
c)
Example 3: Solve by factoring.x2 4x = 45
5.2 Solving, Radicals & i (Miller).notebook
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November 09, 2020
Example 4: Find the zeros of the quadratic function.f(x) = 2x2 11x + 12
Example 5: Use the table below to estimate the solutions of y = x2 + 8.25x + 16.625 .
5.2 Solving, Radicals & i (Miller).notebook
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Vocabulary:Radicand expression under the radical sign
Example 6: Simplify the following square roots.
a) b)
c) d)
e) f)
5.2 Solving, Radicals & i (Miller).notebook
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Example 7: Divide the following radicals.
a) b)
c)
Rationalizing the denominator: the process used to remove the radical from the denominator
Example 8: Rationalize the denominators.
a) b)
5.2 Solving, Radicals & i (Miller).notebook
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Example 9: Simplify. (Add or subtract the following radicals.)
a) b)
Example 10: Find the conjugate of each expression.Conjugate change the sign of the radical part only
a) b)
Rationalize the denominator using the conjugate.
c) d)
5.2 Solving, Radicals & i (Miller).notebook
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Example 11: Simplify Imaginary Square RootsFind the Square root of each number.
a) b)
c)
Example 12: Adding and Subtracting Complex NumbersAdd or subtract. Write the answer in standard form (a+bi).
a) (8i)+(5+4i) b) (76i)(36i)
c) 13(2+7i)+5i
Example 13: Multiplying Complex Numbersa) 4i(6+i) b) (92i)(4+7i)
5.2 Solving, Radicals & i (Miller).notebook
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Example 14: Finding the Complex ConjugateComplex Conjugates the real part stays the same,
the imaginary part is opposite.Find the complex conjugate for each expression.
a) 4+3i b) 32i
Example 15: Multiplying each expression by its complex conjugate.
a) 4+3i b) 32i
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5.2 Solving, Radicals & i (Miller).notebook
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November 09, 2020
5.2 Solving, Radicals & i (Miller).notebook
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November 09, 2020
Homework