Question

Please help ASAP

Use the parabola tool to graph the quadratic function f(x) = -(x-3)(x+1).
Graph the parabola by first plotting it’s vertex and then plotting a second point on the parabola.
picture has the graph.

Answer 1

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: