Answer:
Equation of the parabola: y = -1/4(x - 2)^2 - 2
Explanation:
The vertex form of a quadratic function:
Since we're given the parabola's vertex and a point through which it passes, we can find the equation of the parabola in the vertex form, whose general equation is given by:
y = a(x - h)^2 + k, where:
- (x, y) is any point on the parabola,
- a is a constant determining whether the parabola opens up or down,
- and (h, k) are the coordinates of the vertex.
Finding a and writing the equation of the parabola:
We can find a by substituting (2, -2) for (h, k) and (0, -3) for (x, y) in the vertex form:
-3 = a(0 - 2)^2 - 2
-3 = a(-2)^2 - 2
(-3 = 4a - 2) + 2
(-1 = 4a) / 4
-1/4 = a
Therefore, y = -1/4(x - 2)^2 - 2 is the equation of the parabola with the vertex (2, -2) and that passes through (0, -3).