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Name: Date: Student Exploration: Quadratics in Polynomial Form Activity A:The function ax2 + bx + c Get the Gizmo ready: Be sure Show vertex and intercepts, Show vertex trail, and Show axis of symmetry
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01
Step 1: Start by reading the instructions and understanding the objective of the student exploration quadratics.
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Step 2: Gather all the necessary materials such as a pen or pencil, graph paper, calculator, and any reference materials provided.
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Step 3: Begin by identifying the given quadratic equation or problem to be solved.
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Step 4: Write down the quadratic equation in standard form, which is in the format ax^2 + bx + c = 0.
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Step 5: Determine the values of coefficients 'a', 'b', and 'c' from the given equation.
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Step 6: Use these coefficients to calculate the discriminant, which is b^2 - 4ac. This will help you determine the nature of the roots.
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Step 7: Based on the discriminant, identify whether the quadratic has two real roots, one real root, or no real roots. This information will be helpful in solving the problem.
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Step 8: If the discriminant is positive, use the quadratic formula (-b ± sqrt(b^2 - 4ac)) / (2a) to find the two real roots.
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Step 9: If the discriminant is zero, there is one real root. Use the formula -b / (2a) to find the root.
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Step 10: If the discriminant is negative, there are no real roots, only complex roots. Use the formula (-b ± i*sqrt(-D)) / (2a) to find the complex roots, where 'i' represents the imaginary unit.
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Step 11: Solve the problem by finding the roots or any other relevant information based on the given context.
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Step 12: Check your solution and ensure it satisfies the original equation or problem statement.
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Step 13: If required, present your solution in a clear and organized manner using mathematical notation or graphical representation.
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Step 14: Review and proofread your work before submitting or presenting it as required by your instructor.

Who needs student exploration quadratics in?

01
Students studying quadratic equations in mathematics or algebra courses.
02
Teachers or educators who are designing lesson plans or assessments related to quadratic equations.
03
Researchers or mathematicians who need to explore the properties and applications of quadratic equations.
04
Professionals in fields such as physics, engineering, computer science, or finance that utilize quadratic equations in their work.

What is Student Exploration: Quadratics in Polynomial Form?

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Student exploration quadratics is in the field of mathematics.
Students are required to complete and submit student exploration quadratics assignments.
Student exploration quadratics can be filled out by solving quadratic equations and analyzing the results.
The purpose of student exploration quadratics is to deepen understanding of quadratic functions and their properties.
Students need to report their approach to solving quadratic equations, the solutions obtained, and any patterns observed.
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