Sketch the graph of the quadratic function f(x)=−2x2+6x−3. On the graph, show the values of x and y intercepts, vertex, and axis of the quadratic function. Give the domain and range of the function also.

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Step 1 The given function is f(x)=−2x2+6x−3 Step 2 Here, a=−2,b=6,c=−3. Obtain the vertex as follows: (−b2a,f(−b2a))=(−62(−2),f(−b2a)) =(32,f(32)) =(32,−2(32)2+6(32)−3) =(32,−2(32)2+6(32)−3) =(32,32) Thus,the vertex is (32,32). Note that,the axis of symmetry is a vertical line x=−b2a. Step 3 Obtain the y-intercept as follows: y=−2(0)2+6(0)−3 =−3 Thus, the y-intercept is (0,-3). Obtain the x-intercept as follows: 0=−2x2+6x−3 x1,2=−6±62−4(−2)(−3)2(−2) =−6±12−4 =3−32,3+32 =0.63397,2.36602 Thus, the x-intercepts are (0.63397,0) and (2.36602. 0). From the above figure, its observed that the domain of the function is (−∞,∞) and the range of the function is (−∞,1.5].

Sketch the graph of the quadratic function f(x)=-2x^{2}+6x-3. On the

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