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Understanding Parabolas: Definition and Writing Linear Equations in Parabolic Form

This lesson focuses on the definition of parabolas and the process of writing linear equations in parabolic form. A parabola is defined as the set of all points in a plane that are equidistant from a fixed point (the focus) and a line (the directrix). The goal is to transform a linear equation into parabolic form by grouping terms, completing the square, and simplifying the equation. This method is essential for identifying the vertex, axis of symmetry, and the direction of opening of the parabola for accurate graphing.

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Understanding Parabolas: Definition and Writing Linear Equations in Parabolic Form

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  1. PARABOLAS Topic 7.2

  2. Definition • The set of all points in a plane that are the same distance from a given point called the focus and a given line called the directrix.

  3. Writing linear equation in parabolic form • GOAL: Turn

  4. Writing linear equation in parabolic form • Start with • Group the two x-terms • Pull out the constant with x2 from the grouping • Complete the square of the grouping **Look back to Topic 6.3 for help** • Write the squared term as subtraction so that you end with

  5. Group x-terms Pull out GCF Complete the Square **Remember that whatever you add in the grouping must be subtracted from the c-value** Factor and simplify

  6. Why write in parabolic form?It gives you necessary information to draw the parabola

  7. Graph of prior example

  8. You Try!! Write the following equation in parabolic form. State the vertex, axis of symmetry and direction of opening.

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