The graph of quadratic function f is shown on the grid. The coordinates of the x-intercepts, the y-intercept, and the vertex are all integers.
Quadratic graphed. High point is (1, 4). It also runs through points (-1, 0) and (3,0)
What is the maximum value of f?
The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
Where (h, k) represents the coordinates of the vertex.
Since the vertex is given as (1, 4), the equation for the quadratic function can be written as:
f(x) = a(x - 1)^2 + 4
To find the value of the coefficient a, we can use one of the given points on the graph.
Using the point (-1, 0), we can substitute the coordinates into the equation:
0 = a(-1 - 1)^2 + 4
0 = 4a + 4
4a = -4
a = -1
So the equation for the quadratic function becomes:
f(x) = -(x - 1)^2 + 4
To find the maximum value of f, we need to find the y-coordinate of the vertex. In this case, the maximum value occurs at the vertex, which is given as (1, 4). So the maximum value of f is 4.