Answer:
y = (-4/9)(x - 2)² + 7
Explanation:
To write the equation of a parabola with a vertex at (h, k) and passes through a point (x₁, y₁), you can use the vertex form of a parabolic equation:
y = a(x - h)² + k
Substitute these values into the vertex form equation:
y = a(x - 2)² + 7
Now, use the point (-1, 3) to find the value of 'a':
3 = a(-1 - 2)² + 7
3 = a(-3)² + 7
3 = 9a + 7
Subtract 7 from both sides of the equation:
3 - 7 = 9a
-4 = 9a
Now, divide both sides by 9 to solve for 'a':
a = -4/9
So, the equation of the parabola is:
y = (-4/9)(x - 2)² + 7