Questions: Which function describes the graph?

Solution Steps

The graph shown is a parabola that opens downwards. This indicates that the function is a quadratic function of the form \( y = ax^2 + bx + c \) where \( a < 0 \).

The vertex of the parabola appears to be at the point (0, 5). This suggests that the function can be written in vertex form \( y = a(x - h)^2 + k \), where (h, k) is the vertex. Here, \( h = 0 \) and \( k = 5 \), so the function is \( y = a(x - 0)^2 + 5 \) or \( y = ax^2 + 5 \).

To find the value of 'a', observe another point on the graph. For example, the point (1, 4) lies on the graph. Substitute this point into the equation \( y = ax^2 + 5 \): \[ 4 = a(1)^2 + 5 \] \[ 4 = a + 5 \] \[ a = -1 \]

Final Answer