What is the standard form of $f (x) = (x + 1) (x + 3) + {(- 2 x - 1)}^{2}$ $f(x)=(x+1)(x+3)+(-2x-1)^2$ ?

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What is the standard form of $f (x) = (x + 1) (x + 3) + {(- 2 x - 1)}^{2}$ $f(x)=(x+1)(x+3)+(-2x-1)^2$ ?

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Answer 1 · 2016-02-27T08:38:14

The standard form of this equation is :
$f (x) = 5 x^{2} + 8 x + 4$ $f(x) = 5x^2 + 8x + 4$

Explanation:

The standard form of an equation should look like :
$f (x) = a x^{2} + b x + c$ $f(x) = ax^2 + bx + c$

First, you have to develop the right member : $(x + 1) (x + 3) + {(- 2 x - 1)}^{2}$ $(x+1)(x+3)+(-2x-1)^2$

$[(x \cdot x) + (x \cdot 3) + (1 \cdot x) + (1 \cdot 3)] + [{(- 2 x)}^{2} - 2 \cdot (- 2 x \cdot 1) + 1^{2}]$ $[ (x*x)+(x*3)+(1*x)+(1*3)] + [ (-2x)^2 - 2*(-2x*1) + 1^2]$
Then, we can simplified it :
$[x^{2} + 3 x + x + 3] + [4 x^{2} + 4 x + 1]$ $[ x^2+3x+x+3] + [ 4x^2 + 4x + 1]$
$x^{2} + 4 x + 3 + 4 x^{2} + 4 x + 1$ $x^2+4x+3 + 4x^2 + 4x + 1$
$5 x^{2} + 8 x + 4$ $5x^2+8x+4$

So, $f (x) = 5 x^{2} + 8 x + 4$ $f(x) = 5x^2 + 8x + 4$

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What is the standard form of $f (x) = (x + 1) (x + 3) + {(- 2 x - 1)}^{2}$ $f(x)=(x+1)(x+3)+(-2x-1)^2$ ?

1 Answer

Explanation:

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What is the standard form of $f (x) = (x + 1) (x + 3) + {(- 2 x - 1)}^{2}$ $f(x)=(x+1)(x+3)+(-2x-1)^2$ ?