Questions: Find a formula for the quadratic function depicted in the following graph.

Solution Steps

The vertex of the parabola is the lowest point on the graph. From the graph, the vertex is at the point (0, -12).

The general form of a quadratic function is \( y = ax^2 + bx + c \). Since the vertex form is \( y = a(x - h)^2 + k \), where (h, k) is the vertex, we can write the function as \( y = a(x - 0)^2 - 12 \) or \( y = ax^2 - 12 \).

To find the value of 'a', use another point on the graph. From the graph, we can see that the point (3, -3) lies on the parabola. Substitute this point into the equation \( y = ax^2 - 12 \):

\[ -3 = a(3)^2 - 12 \] \[ -3 = 9a - 12 \] \[ 9a = 9 \] \[ a = 1 \]

Final Answer