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ss_3_1 - Section 3.1 Quadratic Functions Quadratic (second...

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Section 3.1 Quadratic Functions Quadratic (second degree) function: f ( x )= ax 2 + bx + c Example. f ( x )=3 x 2 - 2 x - 2 –2 –1 0 1 2 –2 –1 1 2 Example. g ( x - 2 x 2 +3 x –2 –1 0 1 2 –2 –1 1 2 The graph of a quadratic function is a parabola . Note: The graph of a linear function, f ( x ax + b ,isa straight line . By completing the square, the quadratic y = ax 2 + bx + c can be put in the form y = a ( x + b 2 a ) 2 - b 2 - 4 ac 4 a . For example, by completing the square, 2 x 2 - 3 x +4=2( x - 3 4 ) 2 + 23 8 . When a parabola is the plot of the quadratic y = a ( x + r ) 2 - s , the vertical line given by x = - r is the axis of symmetry of the parabola. For example, the axis of symmetry of the plot of y =3( x - 4) 2 - 2 is the line x =4. Graphing a quadratic function without a graphing calculator. Complete the square Locate the vertex Check whether the graph opens upward or downward Determine the x and y intercepts Draw the graph Example. y =2 x 2 +4 x - 3 y =2[ x 2 +2 x ] - 3 y =2[( x +1) 2 - 1] - 3 y =2( x 2 - 5 vertex at ( x, y )=( - 1 , - 5) 1
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–6 –4 –2 0 2 –4 –2 2 Example. y = - 2 x 2 +4 x - 3 y = - 2[ x 2 - 2 x ] - 3 y = - 2[( x - 1) 2 - 1] - 3 y = - 2( x - 1) 2 - 1 vertex at ( x, y )=(1 , - 1) –2 –1 0 1 2 12 Locating the vertex of a parabola without completing the square: The vertex of the graph of y = ax 2 + bx + c is at the point ( x, y )=( - b 2 a ,f ( - b 2 a )). Example. y =4 x 2 +2 x - 1 a =4, b = 2 implies x = - 2 8 = - 1 4 y = f ( - 1 4 )=4( - 1 4 ) 2 +2( - 1 4 ) - 1= - 5 4 Locating the y -intercept of the graph of a function: Set x = 0 in the formula of the function and solve for y .
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ss_3_1 - Section 3.1 Quadratic Functions Quadratic (second...

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