Answer:
To find an equation for the given graph, let's analyze its characteristics:
- The graph is symmetrical about the y-axis.
- It appears to be a quadratic function opening downwards.
- The vertex of the parabola seems to be at (0, 8).
- It intersects the y-axis at y = 8.
Based on this information, we can write the equation in vertex form:
\[ f(x) = a(x - h)^2 + k \]
Where:
- \( h \) is the x-coordinate of the vertex.
- \( k \) is the y-coordinate of the vertex.
Given that the vertex is at (0, 8), we have \( h = 0 \) and \( k = 8 \).
So, the equation becomes:
\[ f(x) = a(x - 0)^2 + 8 \]
\[ f(x) = ax^2 + 8 \]
To find the value of \( a \), we can use one of the points on the graph. Let's use the point (1, 1):
\[ 1 = a(1)^2 + 8 \]
\[ 1 = a + 8 \]
\[ a = -7 \]
Therefore, the equation for the graph is:
f(x) = -7x^2 + 8