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

--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)

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 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 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)

Given the parabola, write the equation.