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Algebra II w/ trig

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Algebra II w/ trig

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

- 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)

- 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

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!

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.

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

A. y=2x2-8x+6

- Graph
- A.
- B.
- C.
- D.
- E.

How is graphing an inequality different than graphing an equation.

Your line maybe solid or dotted.

You have to shade the correct region.

V. Graph the following inequalities.

y>x2 + 3x -4

y< (x -5)(x+2)

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)