How do you write $F (x) = - x^{2} + 4 x$ $F(x) = -x^2+4x$ in vertex form?

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Answer 1 · 2016-05-20T11:15:30

$y = - {(x - 2)}^{2} + 4 \to g (x) = - {(x - 2)}^{2} + 4$ $y=-(x-2)^2+4 -> g(x) =-(x-2)^2+4$

Standard form $y = a x^{2} + b x + c$ $y=ax^2+bx+c$
Vertex form $y = a {(x + \frac{b}{2 a})}^{2} + k + c$ $y=a(x+b/(2a))^2+k+c$

Where $a {(\frac{b}{2 a})}^{2} + k = 0$ $a(b/(2a))^2+k=0$

$k$ $k$ neutralizes the error introduced
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Step 1 $- 1 (x^{2} - 4 x) + 0$ $" "-1(x^(color(magenta)(2))-4x)+0$

Step 2 $- 1 {(x - 4 x)}^{2} + k + 0$ $" "-1(x-4x)^(color(magenta)(2))+color(magenta)(k)+0$

Step 3 $- 1 {(x - 4)}^{2} + k \leftarrow removed the x from 4 x$ $" "-1(x-4)^2+k" "larr" removed the "x" from "4x$

Step 4 $- 1 {(x - 2)}^{2} + k \leftarrow halved the 4$ $" "-1(x-2)^2+k" "larr" halved the 4"$

Step 4 $k + [- 1 {(- 2)}^{2}] = 0 \to k = + 4$ $" "k+[-1(-2)^2] =0 -> k=+4$

Step 5 $- {(x - 2)}^{2} + 4$ $" "-(x-2)^2+4$

Tony B

How do you write F(x) = -x^2+4xF(x)=−x2+4xF(x) = -x^2+4x in vertex form?