What is the first step when rewriting #y=-4x^2+2x-7# in the form #y=a(x-h)^2+k#?
3 Answers
There is a process for completing the square but the values,
Explanation:
#a = -4# the value of "a" is always the leading coefficient of the#x^2# term.#h=-b/(2a) = -2/(2(-4)) = 1/4# #k = y(h) = y(1/4) = -4(1/4)^2+2(1/4)-7 = -27/4#
This is a lot easier than adding zero to the original equation in the form of
Removing a factor of -4 from the first 3 terms:
Match the middle term of the expansion
Solve for h:
Therefore, we can compress the 3 terms into
Substitute for h:
Combine like terms:
Look at how much easier is it to remember 3 simple facts.
You would factor out the
Explanation:
First complete the square.
get the
You can do this by factoring out
Then complete the square
this simplifies down to
Factor out
Explanation:
In order to complete the square, the coefficient of
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For the sake of completeness the full process is shown below.
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