Answer:
smaller r = -10
larger r = 6
The ordered pair for the vertex of the parabola is [tex](-2,-64)[/tex]
Step-by-step explanation:
We have the function [tex]f(r)=r^2+4x-60[/tex]
In order to factor this quadratic equation, we need to look for two numbers that will
Add together to get 4
Multiply together to get -60
Lets look for the numbers that multiply to give us -60.
-1 and 60
1 and -60
2 and -30
-2 and 30
3 and -20
-3 and 20
4 and -15
-4 and 15
5 and -12
-5 and 12
6 and -10
-6 and 10
Now, we just need to determine which of these numbers will add together to get us 4.
Those two numbers would be -6 and 10.
This means that our factored form of this equation will be
[tex]f(r)=(r-6)(r+10)[/tex]
From this, we can find our roots, which are the solutions to the equation when it is equal to 0.
[tex](r-6)(r+10)=0\\\\r=-10, r=6[/tex]
These are our r values.
The vertex of a parabola will always be directly between the two roots.
The number that is between -10 and 6 is [tex]r=-2[/tex]
To find the y-value of the coordinate pair, we just need to plug -2 into our function.
[tex]f(-2)=(-2)^2+4(-2)-60\\\\f(-2)=4-8-60\\\\f(-2)=-64[/tex]
This means that the ordered pair for the vertex of the parabola is [tex](-2,-64)[/tex]
