1. Warm Up

2. Solving Quadratic Inequalities Algebraically Write and solve the equation obtained by replacing the inequality symbol with an equals sign.

3. 5.8 Modeling with Quadratic Functions p. 306

4. Remember the 3 forms of a quadratic equation! Standard Form y=ax 2 +bx+c Vertex Form y=a(x-h) 2 +k Intercepts Form y=a(x-p)(x-q)

5. Example: Write a quadratic function for a parabola with a vertex of (-2,1) that passes through the point (1,-1). Since you know the vertex, use vertex form! y=a(x-h) 2 +k Plug the vertex in for (h,k) and the other point in for (x,y). Then, solve for a. -1=a(1-(-2)) 2 +1 -1=a(3) 2 +1 -2=9a Now plug in a, h, & k!

6. Example: Write a quadratic function in intercept form for a parabola with x- intercepts (1,0) & (4,0) that passes through the point (2,-6). Intercept Form: y=a(x-p)(x-q) Plug the intercepts in for p & q and the point in for x & y. -6=a(2-1)(2-4) -6=a(1)(-2) -6=-2a 3=a y=3(x-1)(x-4) Now plug in a, p, & q!

7. Example: Write a quadratic equation in standard form whose graph passes through the points (-3,-4), (-1,0), & (9,-10). Standard Form: ax 2 +bx+c=y Since you are given three points that could be plugged in for x & y, write three eqns. with three variables (a,b,& c), then solve using your method of choice such as linear combo, inverse matrices, or Cramer’s rule. 1. a(-3) 2 +b(-3)+c=-4 2. a(-1) 2 +b(-1)+c=0 3. a(9) 2 +b(9)+c=-10 A -1 * B = X =a =b =c