Quadratic function

1. Quadratic function

2. Quadratic function It´s a polynomial function of second degree, whose graph is a curve called parabola. Where a,b and c are constan , c is the interts , a≠0 , c is the y-intercept.

3. Vertex form of the quadratic function (y-k)=(x-h) 2 Where ( h,k ) are the coordinates of the vertex Simmetry axis Vertex ( h,k ) The coordinate x of the vertex ( the h value ) is The coordinate y of the vertex ( the k value ) is f(h)

4. The vertex can be a maximum value or a minimum value . The vertex is maximum if the parabola opens downwards a<0 The vertex is minimum if the parabola opens upwards a>0

5. Solve : f(x)= -x 2 +2x+8 a=-1 b=2 c=8 A) Find the roots (x intercepts ) B) Find the vertex C) Find the y- intercept D) Write the equation of the symmetry axis E) Sketch the graph 0=-x 2 +2x+8 0=-(x 2 -2x-8) 0=(x 2 -2x-8) 0=(x-4)(x+2) Roots are x=4, x=-2 B) Find the vertex ( h,k ) h= -b/2 a = -(2)/2(-1) = 1 k= f(h)= -(1) 2 +2(1)+8 = 9 C) Find the y- intercept c=8 D) Write the equation of the symmetry axis x=1

6. E) Sketch the graph

7. Solve f(x)= 3x 2 -9x-12 A) Find the roots (x intercepts ) B) Find the vertex C) Find the y- intercept D) Write the equation of the symmetry axis E) Sketch the graph f(x)= 3x 2 -9x-12 f(x)= x 2 -4x+4 f(x)= -16x 2 +256x

8. f(x)= 3x 2 -9x-12 f(x)= x 2 -4x+4

9. f(x)= -16x 2 +256x

10. Which of the following equations corresponds to the next graph ?

11. Match each equation with the corresponding graph

12. Find elements of the parabola