Question

Identify the y intercept, identify zeros and rewrite the formula in intercept form. f(x)=x^2+4x-5

Answer 1

First, we need to find the y-intercept. For this, we need to understand that the 'y intercept' refers to the point(s) of the function in which x=0 and y have some value.

So, we set x=0 and obtain:

`y=f(0)=(0)^2+4(0)-5=-5`

So, the function intercepts the y axis on (0,-5)

As for identifying the zeros of the function, this can be done by asking which are the values of x such that f(x)=0. So, if f(x)=0

`\begin{gathered} f(x)=0 \\ \Rightarrow x^2+4x-5=0 \end{gathered}`

And this is simply a quadratic equation, we can choose whatever method we want to solve it, one way is the next:

`\begin{gathered} x^2+4x-5=(x+5)(x-1) \\ \Rightarrow(x+5)(x-1)=0 \end{gathered}`

So, the zeros of the function are x=-5 and x=1

Finally, we need to rewrite the formula in intercept form.

This is a quadratic equation, in general, the intercept form of this kind of functions is:

`y=f(x)=a(x-b)(x-c)`

Where a, b, and c are constants.

So, by finding the zeros of the function, we have already found the intercept form:

`\begin{gathered} f(x)=1\cdot(x+5)(x-1) \\ \begin{cases}a=1 \\ b=-5 \\ c=1\end{cases} \end{gathered}`