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Write the equation of parabola that has vertex (9,7) and passes through point (3,8).

User Huwr
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1 Answer

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Answer:

see explanation

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

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

Here (h, k) = (9, 7), thus

y = a(x - 9)² + 7

To find a substitute (3, 8) into the equation

8 = a(3 - 9)² + 7

8 = 36a + 7 ( subtract 7 from both sides )

36a = 1 ( divide both sides by 36 )

a =
(1)/(36)

y =
(1)/(36)(x - 9)² + 7 ← in vertex form

Expanding the factor and simplifying

y =
(1)/(36)(x² - 18x + 81) + 7

=
(1)/(36) x² -
(1)/(2) x +
(9)/(4) + 7

=
(1)/(36) x² -
(1)/(2) x +
(37)/(4) ← in standard form

User Ildar
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3.3k points