Quadratic function

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Quadratic function

  1. 1. QUADRATIC FUNCTION
  2. 2. QUADRATIC FUNCTION It´s a polynomial function of second degree, whose graph is a curve called parabola. f ( x) a x2 bx c Where a,b and c are constan, c is the interts, a≠0 , c is the y-intercept.
  3. 3. VERTEX FORM OF THE QUADRATIC FUNCTION  (y-k)=(x-h)2 Where (h,k) are the coordinates of the vertex Simmetry axis The coordinate x of the b vertex (the h value) is x 2a The coordinate y of the vertex (the k value) is f(h) Vertex (h,k)
  4. 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. 5. Solve: f(x)= -x2+2x+8 a=-1 b=2c=8A) Find the roots(x intercepts)B) Find the vertexC) Find the y-interceptD) Write the equation of the symmetry axisE) Sketch the graph C) Find the y-intercept c=8A) 0=-x2+2x+8 0=-(x2-2x-8) D) Write the equation of the symmetry axis 0=(x2-2x-8) x=10=(x-4)(x+2)Roots are x=4, x=-2B) Find the vertex(h,k)h= -b/2 a = -(2)/2(-1) = 1k= f(h)= -(1)2+2(1)+8 = 9
  6. 6. E) Sketch the graph
  7. 7. SOLVE F(X)= 3X2-9X-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)= 3x2-9x-12 f(x)= x2-4x+4 f(x)= -16x2+256x
  8. 8. f(x)= 3x2-9x-12 f(x)= x2-4x+4
  9. 9. f(x)= -16x2+256x
  10. 10.  Which of the following equations corresponds to the next graph? a) y 0.5( x 2)( x 4) b) y 0.1( x 6)( x 4) c) y 0.5( x 6)( x 2) d)y 0.1( x 6)( x 4)
  11. 11.  Match each equation with the corresponding graph 2 a) y 0.5 x 2 b) y 0.5 x 2 c) y 0.2 x d)y 2.5 x 2
  12. 12. FIND ELEMENTS OF THE PARABOLA
  13. 13. a) y 0.5( x 2) 2 4b) y 0.5( x 2) 2 4c) y 0.5( x 2) 2 4d)y 0.5( x 2) 2 4

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