Find the equation of the quadratic function f whose graph is shown below.
Ponts on the graph are (-3,-1)(-2,-4)
f(x)=
I don't understand what else do I need to do?
(2,6) (1,4) —> F(x) = ?
To find the equation of a quadratic function, we first need to determine the general form of a quadratic function, which is f(x) = ax^2 + bx + c, where a, b, and c are constants to be determined.
We can use the points (-3, -1) and (-2, -4) to set up a system of equations to solve for a, b, and c.
1. Plug in the x and y values of the first point (-3, -1) into the general equation of a quadratic function:
-1 = a(-3)^2 + b(-3) + c
2. Plug in the x and y values of the second point (-2, -4) into the general equation:
-4 = a(-2)^2 + b(-2) + c
Now we have a system of two equations:
1. -1 = 9a - 3b + c
2. -4 = 4a - 2b + c
Solving this system of equations will give us the values of a, b, and c, which we can then substitute back into the general form of a quadratic function f(x) = ax^2 + bx + c to determine the equation.
To solve the system of equations, there are various methods, such as substitution or elimination. Let's use the elimination method here:
1. Multiply the first equation by 2 and the second equation by 3 to eliminate the c term:
-2 = 18a - 6b + 2c
-12 = 12a - 6b + 3c
2. Subtract the second equation from the first equation:
11 = 6a
3. Divide both sides by 6:
a = 11/6
Now that we have the value of a, we can substitute it back into either of the original equations to find the values of b and c. Let's use the first equation:
-1 = 9(11/6) - 3b + c
-1 = 99/6 - 18b/6 + c
-1 = 99/6 - 18b/6 + c
This equation can be simplified to:
-1 = 33/2 - 3b/2 + c
To solve for c, we need another point. Let's use the point (-3, -1):
-1 = 33/2 - 3b/2 + c
-1 = 33/2 - 9/2 + c
-1 = 24/2 + c
-1 = 12 + c
c = -13
Now we have the values of a, b, and c:
a = 11/6
b = unknown
c = -13
Substituting these values back into the general equation f(x) = ax^2 + bx + c:
f(x) = (11/6)x^2 + (unknown)x - 13
Unfortunately, with the information provided, we cannot determine the exact value of b. Therefore, the equation of the quadratic function f(x) will be in terms of b and can be written as:
f(x) = (11/6)x^2 + bx - 13
y=ax^2+bx + c
first point
-1=9a -3b+c
second point
-2=4a-2b+c
so, two equations, three variables. You need to know y when x is zero to find c.