Question

Can you explain the answers and how to find them and for the vertex don't find it using vertex form.

Answer 1

Solution

- The equation given is

$f(x)=(x+1)(x-5)$

X-intercept:

$\begin{gathered} \text{The x-intercept is when }f(x)\text{ = 0} \\ (x+1)(x-5)=0 \\ \text{ We have to terms whose product is 0. This means that either of }(x+1)\text{ or }(x-5)\text{ must be 0} \\ \\ \text{Thus, we have} \\ x+1=0 \\ OR \\ x-5=0 \\ \\ \therefore x=-1 \\ x=5 \end{gathered}$

Vertex:

$\begin{gathered} f(x)=(x+1)(x-5) \\ \text{Expand} \\ f(x)=x^2-4x-5 \\ \\ f(x)=x^2-4x+(\frac{4}{2})^2-(\frac{4}{2})^2-5 \\ \\ f(x)=x^2-4x+4-4-5 \\ \\ f(x)=(x-2)^2-9 \\ \\ \text{Thus, the vertex is:} \\ (2,-9) \end{gathered}$

Y-intercept:

$\begin{gathered} f(x)=(x+1)(x-5) \\ \text{Expand} \\ f(x)=x^2-4x-5 \\ \\ \text{The y-intercept is when }x=0 \\ f(0)=0^2-4(0)-5 \\ \\ \therefore f(0)=-5 \\ \\ \text{Thus, the y-intercept is }-5 \end{gathered}$

Final Answer

X-intercept:

x = -1, x = 5

Vertex:

(2, -9)

Y-intercept:

y = -5