How do you write $y = - 2 {(x + 1)}^{2} + 3$ $y=-2(x+1)^2 +3$ in standard form?

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How do you write $y = - 2 {(x + 1)}^{2} + 3$ $y=-2(x+1)^2 +3$ in standard form?

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Answer 1 · 2016-07-28T11:41:14

$y = - 2 x^{2} - 4 x + 1$ $y=-2x^2-4x+1$

Explanation:

Consider ${(x + 1)}^{2}$ $" "(x+1)^2$

Write as: $(x + 1) (x + 1)$ $" "color(blue)((x+1))color(brown)((x+1))$

Multiply everything inside the right hand side bracket by everything inside the left hand bracket.

$x (x + 1) + 1 (x + 1)$ $color(brown)(color(blue)(x)(x+1)color(blue)( +1)(x+1))$

$x^{2} + x + x + 1 \to x^{2} + 2 x + 1$ $x^2+x" "+x+1" "->" "x^2+2x+1$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\Rightarrow y = - 2 {(x + 1)}^{2} + 3 \to y = - 2 (x^{2} + 2 x + 1) + 3$ $=>color(brown)(y=-2(x+1)^2+3)color(green)(" "->" "y=-2(x^2+2x+1)+3)$

$\Rightarrow y = - 2 x^{2} - 4 x - 2 + 3$ $=>y=-2x^2-4x-2+3$

$\Rightarrow y = - 2 x^{2} - 4 x + 1$ $=>y=-2x^2-4x+1$

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How do you write $y = - 2 {(x + 1)}^{2} + 3$ $y=-2(x+1)^2 +3$ in standard form?

1 Answer

Explanation:

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How do you write $y = - 2 {(x + 1)}^{2} + 3$ $y=-2(x+1)^2 +3$ in standard form?