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**6.1/6.2/6.6/6.7 Graphing , Solving, Analyzing Parabolas**

Algebra II w/ trig 6.1/6.2/6.6/6.7 Graphing , Solving, Analyzing Parabolas

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**--Vertex: the lowest or highest point of a parabola. **

Quadratic Function has the form y=ax2+bx+c where a cannot be 0 and the graph is a “U-shaped” called a parabola. --ax2: quadratic term --bx: linear term --c: constant term --Vertex: the lowest or highest point of a parabola. --Axis of symmetry: the vertical line through the vertex of parabola. --if a is positive, parabola opens up --If a is negative, parabola opens down --if a > 1, the graph is narrower than the graph of y =x squared --if a <1, the graph is wider than the graph of y =x squared --maximum value: the y-value of its vertex (if the parabola opens down) --minimum value: The y-value of its vertex (if the parabola opens up)

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**Forms for Quadratic Function:**

I. Standard Form Equation: y=ax2 + bx + c A. If a is positive, parabola opens up B. If a is negative, parabola opens down C. The x-coordinate of the vertex is at D. To find the y-coordinate of the vertex, plug the x-coordinate into the given eqn. E. The axis of symmetry is the vertical line x= F. Choose 2 x-values on either side of the vertex x-coordinate. Use the equation to find the corresponding y-values. G. Graph and label the 5 points and axis of symmetry on a coordinate plane. Connect the points with a smooth curve

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**II. Vertex Form Equation: y=a(x-h)2+k**

A. If a is positive, parabola opens up B. If a is negative, parabola opens down. C. The vertex is the point (h,k). D. The axis of symmetry is the vertical line x=h. E. Don’t forget about 2 points on either side of the vertex!

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**III. Intercept Form Equation: y=a(x-p)(x-q)**

A. The x-intercepts are the points (p,0) and (q,0). B. The axis of symmetry is the vertical line x= C. The x-coordinate of the vertex is D. To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. E. If a is positive, parabola opens up If a is negative, parabola opens down. OR—You could just FOIL it, and graph the same way you did the standard equation.

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**IV. Graph: Examples: (notice as you graph which axis the parabola reflects over)**

A. y=2x2-8x+6

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Graph A. B. C. D. E.

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**How is graphing an inequality different than graphing an equation**

How is graphing an inequality different than graphing an equation. Your line maybe solid or dotted. You have to shade the correct region.

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**V. Graph the following inequalities.**

y>x2 + 3x -4 y< (x -5)(x+2)

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**V. Write the equation of the parabola with the given info. A**

V. Write the equation of the parabola with the given info. A. Vertex (2, 3) AND (0,1) B. Vertex (1,3) and (-2, -15)

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**Given the parabola, write the equation.**

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Graphing Quadratic Functions – Concept A quadratic function in what we will call Standard Form is given by: The graph of a quadratic function is called.

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