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Group 5: IRNA SUCIATI K1310044 RINI KURNIASIH K1310069 Mathematics Education ‘10

Quadratic Function. Group 5: IRNA SUCIATI K1310044 RINI KURNIASIH K1310069 Mathematics Education ‘10. Definition. is called quadratic function with variable x http://www.mathmotivation.com. y. Vertex. x. Vertex. Quadratic Functions.

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Group 5: IRNA SUCIATI K1310044 RINI KURNIASIH K1310069 Mathematics Education ‘10

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  1. Quadratic Function Group 5: IRNA SUCIATI K1310044 RINI KURNIASIH K1310069 Mathematics Education ‘10

  2. Definition is called quadratic function with variable x http://www.mathmotivation.com

  3. y Vertex x Vertex Quadratic Functions The graph of a quadratic function is a parabola. A parabola can open up or down. If the parabola opens down, the vertex is the highest point and if the parabola opens up, the vertex is the lowest point

  4. Sketch graph of quadratic function Step: Find the point of intersection a. point intersect y-axis, x=0 then y=ax2 + bx + c =a(0) 2 + b(0) + c = c Therefore point of intersection y-axis is (0,c)

  5. b. The point intersection x-axis. If y=0 or ax2 + bx + c=0. By consider the descriminant to solve the point of intersection. D= b2 -4ac If D>0 then x1≠x2. Hence the graph intersect x-axis “in 2 points that are (x1,0) and (x2,0). If D=0 then x1=x2. Hence the graph intersect x-axis in 1 point that is(x1,0). If D<0 then x value doesn’t satisfying. Hence the graph doesn’t intersect x-axis”. To find the point use the formula

  6. The graph of quadratic function The general of quadratic function form y=ax2 + bx + c

  7. Line of Symmetry y x 2. Find the line of symmetry Parabolas have a symmetric property to them. If we draw a line down the middle of the parabola, we could fold the parabola in half. We call this line of symmetry. When a quadratic function is in standard form y=ax2 + bx + c The equation of the line of symmetry is The line of symmetry ALWAYS passes through the vertex.

  8. 3. Finding the Vertex y = –2x2 + 8x –3 We know the line of symmetry always goes through the vertex. Find the line of symmetry Thus, the line of symmetry gives us the x – coordinate of the vertex. Plug the x – value into the original equation to find the y value. y = –2(2)2 + 8(2) –3 To find the y – coordinate of the vertex, we need to substituted the x – value into the original equation. y = –2(4)+ 8(2) –3 y = –8+ 16 –3 y = 5 Therefore, the vertex is (2 , 5)

  9. 4. Find the other point Find two other points and reflect them across the line of symmetry. Then connect the some points with a smooth curve.

  10. For example: sketch the graph of y = x2 +2x + 1 Solution : Step 1. Find the point of intersection Point of intersection y-axis. If x=0 y = x2 +2x + 1 = (0) 2+2(0)+1 = 1 So the point is (0,1) Point of intersection x-axis. If y=0 y = x2 +2x+1 D=22-4.1.1=0 0= x2 +2x+1 (1 repeated solution) 0= (x-1) 2 So the point is (-1,0)

  11. Step 2. Find the line of symmetry The quadratic equation y= x2 +2x + 1 so the line of symmetry So the line of symmetry is x=-1

  12. x y -3 4 1 4 Step 3. Find the vertex Substitude the line of symmetry x=-1 to quadratic equation y= x2 +2x + 1 y=(-1) 2+2(-1)+1 y=0 So the vertex is (-1,0) Step 4. The other point y= x2 +2x + 1

  13. The sketch of the quadratic function y= x2 +2x + 1

  14. THANK YOU References: http://www.mathmotivation.com Maryanto. 2008. Matematika X. Jakarta: Departemen Pendidikan Nasional.

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