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AURORKA [14]
2 years ago
7

Equation of the parabola in vertex form that passes through (4,-7) and has a vertex of (1,-6)

Mathematics
1 answer:
Alina [70]2 years ago
7 0

y = -\frac{1}{9}(x - 1)^2 - 6

Step-by-step explanation:

The vertex form of the equation for a parabola is given by

y = a(x - h)^2 + k

where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as

y = a(x - 1)^2 - 6

Also, since the parabola passes through (4, -7), we can use this to find the value for a:

-7 = a(4 - 1)^2 - 6 \Rightarrow -7 = 9a - 6

or

a = -\frac{1}{9}

Therefore, the equation of the parabola is

y = -\frac{1}{9}(x - 1)^2 - 6

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