Answer:
Equation of the parabola: y = (2/9)(x - 5)² - 3
y-coordinate for the y-intercept: 23/9
Step-by-step explanation:
The equation of a parabola with vertex (h, k) is
y = a(x - h)² + k
Where a is a constant value.
Replacing the vertex (h, k) = (5, -3), we get:
y = a(x - 5)² - 3
Now, to find the value of a, we will replace (x, y) by the given point (2, -1)
-1 = a(2 - 5)² - 3
Solving for a, we get:
-1 = a(-3)² - 3
-1 = a(9) - 3
-1 + 3 = 9a - 3 + 3
2 = 9a
2/9 = 9a/9
2/9 = a
Therefore, the value of a is 2/9 and the equation of the parabola is
y = (2/9)(x - 5)² - 3
Now, to know the y-coordinate for the point where the parabola intersects the y-axis, we need to replace x by 0, so
y = (2/9)(0 - 5)² - 3
y = (2/9)(-5)² - 3
y = (2/9)(25) - 3
y = 50/9 - 3
y = 23/9
So, the answers are:
Equation of the parabola: y = (2/9)(x - 5)² - 3
y-coordinate for the y-intercept: 23/9