Question

Consider the quadratic function f(x)=−x^2+4x+12

Determine the following:

The smallest xx-intercept is x=Incorrect
The largest xx-intercept is x=
The yy-intercept is y=

Answer 1

• The smallest x-intercept is x= -2

• The largest x-intercept is x= 6

• The y-intercept is y= 12

Explanation:

We are given a function as follows:

`y=f(x)=-x^2+4x+12`

The x-intercept of a function is the value of x where the function is equal to 0.

i.e.

`y=f(x)=0`

`-x^2+4x+12=0`

i.e.

`x^2-4x-12=0\\\\x^2-6x+2x-12=0`

( We used the method of splitting the middle term)

`x(x-6)+2(x-6)=0\\\\(x+2)(x-6)=0`

i.e.

`x=-2\ and\ x=6`

Hence, the smallest x-intercept is: x= -2

and the largest x-intercept is: x=6

The y-intercept is the value of y where x=0

i.e. we have:

`y=-0^2+4* 0+12\\\\y=12`