Function Challenge 5

Algebra Level 2

Denote 2 functions f ( x ) = x 2 + 3 x − 2 f(x)=x^2+3x-2 and g ( x ) = − x 2 + 5 x − 7 g(x)=-x^2+5x-7 , what can you conclude about the graphs of f ( x ) f(x) and g ( x ) g(x) ?

This is one part of 1+1 is not = to 3 .
The 2 graphs intersect each other at 2 distinct points The 2 graphs intersect each other exactly at 1 point The 2 graphs do not meet each other at all Not enough information Cheese

Kenneth Tan by Kenneth Tan , 21, Malaysia

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1 solution

Kay Xspre
Mar 21, 2016

If considering ( f − g ) ( x ) (f-g)(x) to find common roots (which is where the graph will intersect), we get that ( f − g ) ( x ) = 2 x 2 − 2 x + 5 = 2 ( x − 1 2 ) 2 + 9 2 (f-g)(x) = 2x^2-2x+5 = 2(x-\frac{1}{2})^2+\frac{9}{2}

This ( f − g ) ( x ) (f-g)(x) does not have a root, so f ( x ) f(x) and g ( x ) g(x) does not have common root, which means they will not touch each other in any way. Alternatively, this question may be solved by plotting graph

Left-handed is \(y = x^2+3x-2\); Right-handed is \(y = -x^2+5x-7\). Both graphs does not touch each other Left-handed is y = x 2 + 3 x − 2 y = x^2+3x-2 ; Right-handed is y = − x 2 + 5 x − 7 y = -x^2+5x-7 . Both graphs does not touch each other

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