The graph of a quadratic function is shown on the grid.
graph of a parabola through (-4,0), (-3,4) and (0,4)
What function is best represented by this graph?
The graph of a quadratic function is shown on the grid.
graph of a parabola through (-4,0), (-3,4) and (0,4)
What function is best represented by this graph?
f(x)=-(x-1)(x+4)
f(x)=(x+1)(x-4)
f(x)=-(x+1)(x-4)
f(x)=(x-1)(x+4)
To determine the function that best represents the graph of the parabola passing through the points (-4,0), (-3,4), and (0,4), we can use the general form of a quadratic function, f(x) = ax^2 + bx + c, where a, b, and c are constants.
Using the three given points to form a system of equations:
When x = -4, y = 0:
0 = a(-4)^2 + b(-4) + c
16a - 4b + c = 0
When x = -3, y = 4:
4 = a(-3)^2 + b(-3) + c
9a - 3b + c = 4
When x = 0, y = 4:
4 = a(0)^2 + b(0) + c
c = 4
Substitute c = 4 into the first two equations:
16a - 4b + 4 = 0
9a - 3b + 4 = 4
Simplify the equations further:
16a - 4b = -4
9a - 3b = 0
Now, we can solve this system of equations to determine the values of a and b. Once we have those values, we can write the function in the form f(x) = ax^2 + bx + c to best represent the given graph.