Determine the quadratic function f whose graph is given.
The vertex is (-3,-13) and the y-intercept is -4
f(x)=
To determine the quadratic function f, we can use the standard form of a quadratic equation:
f(x) = a(x - h)^2 + k,
where (h, k) represents the vertex of the parabola.
Given that the vertex is (-3, -13), we can substitute these values into the equation:
f(x) = a(x - (-3))^2 + (-13).
f(x) = a(x + 3)^2 - 13.
We also know that the y-intercept is -4, which means when x = 0, y = -4. Substituting these values into the equation:
-4 = a(0 + 3)^2 - 13.
-4 = a(3)^2 - 13.
-4 = 9a - 13.
9a = -4 + 13.
9a = 9.
Solving for 'a', we divide both sides of the equation by 9:
a = 9 / 9.
a = 1.
Now that we have the value of 'a', we can substitute it back into the equation:
f(x) = 1(x + 3)^2 - 13.
f(x) = (x + 3)^2 - 13.
Therefore, the quadratic function f(x) is f(x) = (x + 3)^2 - 13.
f(x) = a(x+3)^2 - 13
since f(0) = -4,
-4 = 9a-13
a = 1
f(x) = (x+3)^2 - 13