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Lesson Objective(s)
- Graph quadratic functions.
- Recognize that a quadratic function has the shape of a parabola.
- Find the coordinates of the vertex of a parabola.
- Recognize whether the vertex of a parabola represents a minimum or a maximum.
- Find the equation of the axis of symmetry.
- Find the x and y-intercepts of a quadratic function.
- Recognize standard form of a quadratic function.
- Recognize factored form of a quadratic function.
- Recognize vertex form of a quadratic function.
- Determine which forms of a quadratic function are best used for solve a problem.
- Recognize perfect square quadratic equations.
- Create perfect square quadratic equations.
- Solve quadratic equations using completing the square.
- Use key features of quadratic graphs to solve real-world problems.
- Connect real-world measurements to quadratic equations.
- Explain why the sum of two square roots is not equal to the square root of their sum.
- Convert expressions to simplest radical form.
- Use conjugate radicals to simplify radical expressions.
- Solve radical equations ensuring to test for extraneous solutions.
- Explain each step taken in solving radical equations.
- Determine the distance between two points given their coordinates.
- Determine a coordinate based on the known distance and a known coordinate.
- Simplify nth root radicals.
- Solve nth root radicals.
Standard(s)
- CC.9-12.A.REI.2 Understand solving equations as a process of reasoning and explain the reasoning. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
- CC.9-12.N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.
- CC.9-12.N.RN.2 Extend the properties of exponents to rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- CC.8.G.8 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Mathematical Practice(s)
- #1 - Make sense of problems and persevere in solving them
- #2 - Reason abstractly and quantitatively
- #7 - Look for and make use of structure
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