Find the equation of a quadratic function whose graph is a parabola passing through the points (−2,−9), (2,7), and (4,−9).

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Derrick · Accepted Answer

Let the quadratic equation be y=ax2+bx+c    Now,     The equation passing through the points (−2,−9), (2,7), and (4,−9).    That is,     At point (−2,−9):     y=ax2+bx+c    ⇒−9=a(−2)2+b(−2)+c    ⇒4a–2b+c=−9         ........(i)    At point (2,7):     y=ax2+bx+c    ⇒7=a(2)2+b(2)+c    ⇒4a+2b+c=7         ........(ii)    At point (4,−9):     y=ax2+bx+c    ⇒−9=a(4)2+b(4)+c    ⇒16a+4b+c=−9         ........(iii)    Subtract equation (i) from (ii):     (4a+2b+c)–(4a–2b+c)=7−(−9)    ⇒4b=16    ⇒b=164    ⇒b=4     Subtract four times of equation (ii) from equation (ii):     (16a+4b+c)−4(4a+2b+c)=−9–4×7    ⇒−4b–3c=−37    ⇒−4×4–3c=−37    ⇒−3c=−37+16    ⇒−3c=−21    ⇒c=−21−7    ⇒c=7    Put the value of b and c in equation (i):     4a–2b+c=−9    ⇒4a–2×4+7=−9    ⇒4a=−8    ⇒a=−84    ⇒a=−2    The values of constants are: a=−2, b=4, c=7    Therefore,     The required equation of quadratic function is:     y=−2x2+4x+7

Find the equation of a quadratic function whose graph is a parabola passing thro

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