Write the equation of the quadratic function f(x) that satisfies all three properties below: contains the point (5, −3) has the shape =0x2 The x- coordinate of the vertex is -4

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Write the equation of the quadratic function f(x) that satisfies all three properties below: contains the point (5, −3) has the shape =0x2   The x- coordinate of the vertex is -4

George Woody · Accepted Answer

Step 1  Given  The function f(x) that satisfies all three properties below:  1) contains the point (5, −3)  2) has the shape =0x2  3) The x- coordinate of the vertex is -4  Step 2  To find quadratic function  Use vertex form of the quadratic equation y=a(x−h)2+k, where (h, k) is vertex .  Here h is vertex x coordinate also a=1,  So h=−4, x=5 and y=−3  Plug h=−4, x=5 and y=−3 in vertex form of the quadratic equation.  −3=(5−(−4))2+k  −3=(9)2+k  −3=81+k  k=−3−81  k=−84  So quadratic equation become  y=(x+4)2−84  y=x2+8x+16−84  y=x2+8x−68  Therefore , The quadratic equation is y=x2+8x−68

Write the equation of the quadratic function f(x) that satisfies

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