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Convert the function from standard form to vertex form. Give the equation in vertex form and the vertex. f(x) =-3x^2 +12x-7

User Nii Mantse
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1 Answer

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Answer:

see explanation

Explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

given

f(x) = 3x² + 12x - 7 ← factor out 3 from the first 2 terms

= 3(x² + 4x) - 7

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 4x

f(x) = 3(x² + 2(2)x + 4 - 4) - 7

= 3(x + 2)² - 3(4) - 7

= 3(x + 2)² - 12 - 7

= 3(x + 2)² - 19 ← in vertex form

with vertex = (- 2, - 19 )

User Amit Tomar
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