What is the equation of a quadratic function whose graph passes through (2,0), (5,0), and (3,−8)? Write your equation in standard form.

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okomgcae · Accepted Answer

Consider the given:   The graph passes through (2,0), (5,0) and (3,−8).   Let the equation is y=ax2+bx+c.   Consider the point (2,0),   a(2)2+b(2)+c=0  4a+2b+c=0         ... ... (1)  Consider the point (5,0),   a(5)2+b(5)+c=0  25a+5b+c=0       ... ... (2)  Consider the point  (3,−8),   a(3)2+b(3)+c=−8  9a+3b+c=−8        ... ... (3)  From equation (1) and (2),   4a+2b+c=25a+5b+c  4a+2b=25a+5b  a–25a=5b–2b  −7a=b  From equation (1),   4a+2b+c=0  4a+2(−7a)+c=0  4a–14a+c=0  −10a+c=0  c=10a  Substitute the value of b and c in equation (3).   9a+3b+c=−8  9a+3(−7a)+(10a)=−8  9a–21a+10a=−8  −21a+19a=−8  −2a=−8  a=4  b=−7a  b=−7(4)  b=−28  c=10a  c=10(4)  c=40  Hence, The equation of quadratic function will be:   y=4x2–28x+40

What is the equation of a quadratic function whose graph passes through \left

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