What is the vertex form of y= 5x^2-2x – 6 ?

1 Answer
Jul 29, 2016

See explanation

Explanation:

color(blue)("Step 1")

Write as: y=5(x^2-2/5x)-6+k

where k is a correction for an error that will be introduced by the method.
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color(blue)("Step 2")
color(brown)("Move the power to outside the brackets")

y=5(x-2/5x)^2-6+k
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color(blue)("Step 3")
color(brown)("Halve the "2/5)

y=5(x-2/10x)^2-6+k
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color(blue)("Step 4")
color(brown)("Remove the "x" from "-2/10x)

y=5(x-2/10)^2-6+k

color(green)("Now we need to determine the value of "k)
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color(blue)("Step 5")

The squaring the -2/10" " ->+4/100

Now multiply it by the 5 ->5xx4/100 = 4/20-=1/5

So 1/5+k=0=> k=-1/5 giving

" "color(purple)(bar(ul(|color(white)((2/2)/2)y=5(x-1/5)^2-31/5color(white)(2/2)|)))

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color(white)(.)

Tony B