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How do you write #y = 4x^2-8x-6# into vertex form?

Answer 1

Avery Alexander

#y=4x^2-8x-6=4(x-1)^2-10#.

In general #ax^2+bx+c = a(x+b/(2a))^2+(c-b^2/(4a)).#

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Answer 2

Savannah Anderson

To write the quadratic equation ( y = 4x^2 - 8x - 6 ) into vertex form, follow these steps:

Factor out the leading coefficient from the ( x^2 ) and ( x ) terms: ( y = 4(x^2 - 2x) - 6 ).
Complete the square inside the parentheses by adding and subtracting ( (b/2)^2 ), where ( b ) is the coefficient of the ( x ) term: ( y = 4(x^2 - 2x + 1 - 1) - 6 ).
Rewrite the equation with the completed square term factored: ( y = 4((x - 1)^2 - 1) - 6 ).
Expand the equation: ( y = 4(x - 1)^2 - 4 - 6 ).
Simplify: ( y = 4(x - 1)^2 - 10 ).

So, the vertex form of the equation ( y = 4x^2 - 8x - 6 ) is ( y = 4(x - 1)^2 - 10 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.