Question

Consider the quadratic function f(x)=−x^2+x+30

Determine the following:

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

Answer 1

Answer and Explanation:

Given : The quadratic function
`f(x)=-x^2+x+30`

To find : Determine the following ?

Solution :

The x -intercept are where f(x)=0,

So,
`-x^2+x+30=0`

Applying middle term split,

`-x^2+6x-5x+30=0`

`-x(x-6)-5(x-6)=0`

`(x-6)(-x-5)=0`

`x=6,-5`

The x-intercepts are (6,0) and (-5,0).

The smallest x-intercept is x=-5

The largest x-intercept is x=6

The y -intercept are where x=0,

So,
`f(0)=-(0)^2+0+30`

`f(0)=30`

The y-intercept is y=30.