9-2 Quadratic Functions

Objective

To graph quadratic functions of the form y = a x 2 + b x + c y equals , eh x squared , plus b x plus c

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The parabola in the Solve It has the equation h = − 16 t 2 + 32 t + 4 . h equals negative , 16 t squared , plus 32 t plus 4 .  Unlike the quadratic functions you saw in previous lessons, this function has a linear term, 32t.

Essential Understanding In the quadratic function y = a x 2 + b x + c , y equals , eh x squared , plus b x plus c comma  the value of b affects the position of the axis of symmetry.

Consider the graphs of the following functions.

• y = 2 x 2 + 2 x y equals , 2 x squared , plus 2 x

  

• y = 2 x 2 + 4 x y equals , 2 x squared , plus 4 x

  

• y = 2 x 2 + 6 x y equals , 2 x squared , plus 6 x

  

Notice that the axis of symmetry changes with each change in the b-value. The equation of the axis of symmetry is related to the ratio b a . b over eh , .

equation : y = 2 x 2 + 2 x y = 2 x 2 + 4 x y = 2 x 2 + 6 x b a : 2 2 = 1 4 2 = 2 6 2 = 3 axis of symmetry: x = − 1 2 x = − 1   or   − 2 2 x = − 3 2 table with 3 rows and 4 columns , row1 column 1 , equation , colon , column 2 y equals 2 , x squared , plus 2 x , column 3 y equals 2 , x squared , plus 4 x , column 4 y equals 2 , x squared , plus 6 x , row2 column 1 , b over eh , colon , column 2 2 halves , equals 1 , column 3 4 halves , equals 2 , column 4 6 halves , equals 3 , row3 column 1 , axisofsymmetrycolon , column 2 x equals negative , 1 half , column 3 x equals negative 1 or minus , 2 halves , column 4 x equals negative , 3 halves , end table

The equation of the axis of symmetry is x = − 1 2 ( b a ) , x equals negative , 1 half . open , b over eh , close . comma  or x = − b 2 a . x equals . fraction negative b , over 2 eh end fraction . .

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