Question

f(x)=(−x+3)(x+5)Use the Parabola tool by plotting the vertex first and then another point on the parabola.

Answer 1

Step-by-step explanation:

Here, we want to get the plot of the parabola

We start by getting its vertex

We have that as follows:

`\begin{gathered} f(x)\text{ = (-x+3)(x+5)} \\ f(x)=-x^2-2x+15 \end{gathered}`

We have the vertex form as follows:

`\begin{gathered} f(x)\text{ = }-1(x+1)^2+16 \\ \text{compared with the general vertex form:} \\ f(x)=a(x-h)^2+k \\ \text{vertex is (h,k)} \end{gathered}`

The vertex here is thus (-1,16)

To get the other point, we can equate the values in the brackets to zero and solve for x

We have that as:

`\begin{gathered} -x+3\text{ = 0} \\ x\text{ = 3} \\ x+5\text{ = 0} \\ x=\text{ -5} \end{gathered}`

The other points are thus (3,0) and (-5,0)

Thus, we can join (-1,16) with either (3,0) and (5,0) as shown below: