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Answer:
Step-by-step explanation:
There are two ways to solve this problem: The easiest would be to put the equation into a graphing calculator. You can also change the equation into standard form in order to figure out how to graph the function.
y = -(x - 3)(x + 1)
First let's change the function into standard form:
y = ax^2 + bx + c
Use the FOIL method to distribute the variables inside the parentheses
y = -(x - 3)(x + 1)
y = - (x^2 - 2x - 3)
Distribute the -1
y = -x^2 + 2x + 3
The coordinates for the vertex can be represented as (h,k)
Now that we know the values of a = -1 and b = 2, we can find the value of h.
h = -b/2a
Replace the variables with their known values
h = -2/ 2(-1)
Solve
h = -2/-2 = 1
Use the value of h = 1 and put it back into the original equation to find the value of k.
y = -(x - 3)(x + 1)
Replace x with h = 1.
k = -(1 - 3)(1 + 1)
Solve
k = -(-2)(2) = 4
Now we can graph the function using the values of a, h, and k.
a = -1 h = 1 k = 4
The coordinate of the vertex is (1,4) and the graph opens downwards because the slope is negative.
Here is the function graphed:
