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Y = x^2+ 7x - 5 can be written in the form y = (x + a)^2+b

Find the value of a and the value of b

1 Answer

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Answer:

see explanation

Explanation:

The equation of a parabola in vertex form is

y = (x - h)² + k (h, k) are the coordinates of the vertex

Given y = x² + 7x - 5

To express in vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )²

y = x² + 2(
(7)/(2) )x +
(49)/(4) -
(49)/(4) - 5

y = (x +
(7)/(2) )² -
(49)/(4) -
(20)/(4)

y = (x +
(7)/(2) )² -
(69)/(4)

Hence

a =
(7)/(2) and b = -
(69)/(4)

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