Hello!
The answer is A.x-int : (–4, 0), (–5, 0); y-int : (0, 20)
Why?
To find the X and Y interceptions of a function, we need to calculate when the function tends to 0.
To identify the X interception we have to make Y equal to 0, so we have the first equation:
[tex]0=X^2+9x+20\\[/tex] - This equation is a quadratic equation and it can be easily solved by using the quadratic formula.
Quadratic formula : [tex]x=\frac{-b ±\sqrt{b^2-4*a*c} }{2*a}[/tex]
Where:
- a is equal to the quadratic term coefficient
- b is equal to the lineal term coefficient
- c is equal to the constant number
So, from our quadratic equation we know that:
[tex]a=1\\b=9\\c=20[/tex]
By substituting in the quadratic formula, we have:
[tex]x=\frac{-9 ±\sqrt{9^2-4*1*20} }{2*1}\\[/tex]
[tex]x=\frac{-9±\sqrt{81-80} }{2} \\\\x=\frac{-9±1 }{2}\\\\x1=\frac{-9+1}{2} =-4\\\\x2=\frac{-9-1}{2} =-5[/tex]
So, we know that x tends to 0 at -4 and -5
X intercepts at (-4,0) and (-5,0)
In order to know when y intercepts, we have to make x equal to 0
Making x equal to 0, we have
[tex]y=0^2+9*0+20\\\\y=20[/tex]
So, now we know that y tends to 0 at 20
Y intercepts once at (0,20)
Have a nice day!
