Question

Which function is a quadratic function?

P(x)=2x(×^2+6)+1
M(x)=-4(x+3)-2
t(x)=-8x^2(x^2-6+1
H(x)=3x(x-2)-4

Answer 1

The correct answer is: [D]: " H(x) = 3x(x - 2) - 4 " .
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Note: A "quadratic function" takes the form of:
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f(x) = ax² + bx + c ;
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Answer choice: [D]: " H(x) = 3x(x - 2) - 4 " ;

takes this form:
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" H(x) = 3x(x - 2) - 4 " ;

→ " 3x(x - 2) - 4 " ;

Note the "distributive property" of multiplication:
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a(b + c) = ab + ac ; AND

a(b - c) = ab - ac ;
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→ As such;

" 3x(x - 2) = (3x * x) - (3x * 2) = 3x² - 6x;

So, we can rewrite the expression:

→ " 3x(x - 2) - 4 " ;

as: → " 3x² - 6x - 4 ;

And the entire function as:

H(x) = 3x(x - 2) - 4 ;

as:

H(x) = 3x² - 6x - 4 ;

Which takes the form of a "quadratic function" ;

→ f(x) = ax² + bx + c ;

in which: a = 3 ; b = - 6 ; c = - 4 .
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