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A polynomial equation

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Where a parabola makes its sharpest turn: the "peak" of the parabola.

It is on the parabola's axis of symmetry.

(h, k)

Math Is Fun - Parabolic Vertex

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Grade 9

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Like a U.

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Parabolic Icon

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Includes TEKS tested in lesson.
Previous Assignment - Google Doc

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§111.40. Algebra II

(c)  Knowledge and skills.

(4)  Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:

(B)  write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening

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Can solve for roots by factoring, quadratic formula, or completing the square.

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How we describe a function.

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How do I determine the direction of opening?

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How do I determine the direction of opening?

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A fixed point that describes the distance to the curve of a parabola of any point.

Applied to a parabola's reflector property.

Vertical: (h, k+1/(4a))
Horizontal: (h+1/(4a), k)

Math Is Fun - Parabola

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How are the focus and directrix related? 

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How are the focus and directrix related? 

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A parabola is the set of points in a plane that are the same distance from a given point (focus) and a given line (directrix) in that plane.

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Any ray parallel to the axis of symmetry gets reflected off the surface straight to the focus.

And that explains why that dot is called the focus ...

... because that's where all the rays get focused!

Math Is Fun - Parabola

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A fixed straight line that describes the distance to the curve of the parabola of any point.

Vertical: y=k-1/(4a)
Horizontal: x=h-1/(4a)

Math Is Fun - Parabola

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Equation of a Parabola (Direction of Opening)

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Equation of a Parabola (Direction of Opening)

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The equation used will convey which direction the parabola will open.

Vertical: y=a(x – h)² + k

Up: +a

Down: -a

Horizontal: x = a(y – k)² + h

Left: -a

Right: +a

CliffNotes - Parabola
MathWords - Parabola

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The line passing through the focus and vertex of a parabola. The axis of symmetry is perpendicular to the directrix.

Vertical: x=h
Horizontal: y=k

CliffNotes - Parabola

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How do I write the equation of a parabola?

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How do I write the equation of a parabola?

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Vertically and horizontally

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We can plug all this information into the equation to be able to graph the function without a calculator, but by hand.

On the other hand, information given by the graph or equation can allow us to solve for its characteristics.

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TEKS

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Algebra II Workbook for Dummies

TExES Mathematics 7-12 (235) Secrets Study Guide