QUADRATIC FUNCTION Given a Function y = 2x2 -6x -8 in domain

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Presentation transcript:

QUADRATIC FUNCTION Given a Function y = 2x2 -6x -8 in domain D= { x|-3 ≤ x ≤ 6}, Draw the graph of that function! Solution : The Intercepts i. X- Intercepts ,Y=0, so 2x2 -6x -8 =0 x2- 3x -4 =0 →(x-4)(x+1)=0 the x-intercepts are x=4 and x=-1 then A (4,0) and B( -1,0) ii. Y- Intercepts, x=0, y = 2x2 -6x -8, y = 2.02 -6.0 -8 =-8 The intercepts is y =-8 , the C = ( 0,-8 )

Next b. The axis of parabola x = -b/2a = -(-6) /2.2 = 3/2 c. The Vertex V (x,y) , V ( -b/2a, -D/-4a) x = -b/2a = 3/2 y = -D/4a = -(b2-4ac)/4a = -(36+64)/4.2 = - 12 ½ V ( 3/2 , -12 ½ ) V is minimum point because a= 2 (a>0) so parabola is Upward

Next The Conclusion : X – intercepts A ( 4,0), B (-1,0) d. The point which satisfy the function The Conclusion : X – intercepts A ( 4,0), B (-1,0) y – intercepts C ( 0,-8) Axis parabola x = 3/2 Vertex D ( 3/2, -12 ½ ) x -3 -2 -1 1 2 3 4 5 6 y 28 12 -8 -12

The Graph

About The Graph The Parabola Y= ax2+bx+c Upward or downward, Depend on the value of a If a> 0 and a<0

About The Graph… Vertex When We called Maximum or Minimum ? Maximum Minimum Downward Upward a<0 a>0

Resume About the Graph….

Resume about the graph… Definitif Negatif