Graph each quadratic function using the steps from the picture. Based on the graph determine t and range of the quadratic function. F(x)=4x2−4x−3

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Graph each quadratic function using the steps from the picture. Based on the graph determine t and range of the quadratic function.  F(x)=4x2−4x−3

juniorekze · Accepted Answer

Step1 To draw graph of the quadratic equation F(x)=4x2−4x−3 Step2 Compare given function with f(x)=ax2+bx+c a=4 b=−4 c=−3 1) Since a&amp;gt;0 graph is open upwards Step3 2.) vertex=(−b2a,F(−b2a)) −b2a=−(−4)2×4 −b2a=0.5 F(0.5)=4(0.5)2−4(0.5)−3 F(0.5)=−4 vertex=(0.5,−4) axis of symmetry x=−b2a x=0.5 Step 4 3.) y-intercept F(0)=0−0−3 F(0)=−3 y-intercept is (0, -3) Step 5 4) b2=4ac=(−4)2−4(4)(−3) b2−4ac=16+48 b2−4ac=64 b2−4ac&amp;gt;0 Thus, F(x) has two x-intercept F(x)=0 4x2−4x−3−0 4x2−6x+2x−3=0 2x(2x−3)+1(2x−3)=0 (2x+1)(2x−3)=0 x=−12,32 x=−0.5,1.5 x-intercept are (-0.5,0) and (1.5,0)  &amp;lt;br/&amp;gt; Domain of the given function is &amp;lt;span class=&quot; /&amp;gt;(−∞,∞) Range of the given function is [−4,∞)

Graph each quadratic function using the steps from the picture.

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