1. 4.2A Graph Quadratic Functions in Vertex or Intercept Form Algebra II Algebra II

2. Vertex Form Equation y=a(x-h)2+k If a is positive, parabola opens up If a is negative, parabola opens down. The vertex is the point (h,k). The axis of symmetry is the vertical line x=h. Don’t forget about 2 points on either side of the vertex! (5 points total!)

3. Example 1: Graph y=-.5(x+3) 2 +4 a is negative (a = -.5), so parabola opens down. a is negative (a = -.5), so parabola opens down. Vertex is (h,k) or (-3,4) Vertex is (h,k) or (-3,4) Axis of symmetry is the vertical line x = -3 Axis of symmetry is the vertical line x = -3 Table of values x y Table of values x y -1 2 -1 2 -2 3.5 -2 3.5 -3 4 -3 4 -4 3.5 -4 3.5 -5 2 -5 2 Vertex (-3,4) (-4,3.5) (-5,2) (-2,3.5) (-1,2) x=-3

4. Now you try one! Ex. 2 y=2(x-1) 2 +3 Open up or down? Open up or down? Vertex? Vertex? Axis of symmetry? Axis of symmetry? Table of values with 5 points? Table of values with 5 points?

5. (-1, 11) (0,5) (1,3) (2,5) (3,11) X = 1

6. Intercept Form Equation y=a(x-p)(x-q) The x-intercepts are the points (p,0) and (q,0). The x-intercepts are the points (p,0) and (q,0). The axis of symmetry is the vertical line x= The axis of symmetry is the vertical line x= The x-coordinate of the vertex is The x-coordinate of the vertex is To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. If a is positive, parabola opens up If a is positive, parabola opens up If a is negative, parabola opens down.

7. Example 3: Graph y=-(x+2)(x-4) Since a is negative, parabola opens down. The x-intercepts are (-2,0) and (4,0) To find the x-coord. of the vertex, use To find the y-coord., plug 1 in for x. Vertex (1,9) The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex)The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex) x=1 (-2,0)(4,0) (1,9)

8. Now you try one! Ex. 4 y=2(x-3)(x+1) Open up or down? Open up or down? X-intercepts? X-intercepts? Vertex? Vertex? Axis of symmetry? Axis of symmetry?

9. (-1,0)(3,0) (1,-8) x=1

10. 4.2B Changing from vertex or intercepts form to standard form The key is to FOIL! (first, outside, inside, last) The key is to FOIL! (first, outside, inside, last) Ex 1: y=-(x+4)(x-9)Ex 2: y=3(x-1) 2 +8 Ex 1: y=-(x+4)(x-9)Ex 2: y=3(x-1) 2 +8

11. Ex 1: y=-(x+4)(x-9) Ex 2: y=3(x-1) 2 +8 =-(x 2 -9x+4x-36) =3(x-1)(x-1)+8 =-(x 2 -5x-36) =3(x 2 -x- x+1)+8 =-(x 2 -5x-36) =3(x 2 -x- x+1)+8 y=-x 2 +5x+36 =3(x 2 -2x+1)+8 Min. or max. ? =3x 2 -6x+3+8 y=3x 2 -6x+11 y=3x 2 -6x+11 Min. or max?

12. Assignment