Some possible questions:
1. What are the x and y intercepts for this equation?
a) The y intercept is the value of the equation when x=0
In this case if x=0
color(white)("XXX")F(0)=0^2+6xx0+8=8
So the y intercept is 8
b) The x intercepts are the values of x for which the equation is equal to 0
In this case if x^2+6x+8=0
color(white)("XXX")We can factor the expression on the left:
color(white)("XXX")(x+2)(x+4)=0
color(white)("XXX")rarr{:((x+2)=0,color(white)("xx")"or"color(white)("xx"),(x+4)=0),
(rarr x=-2,,rarr x=-4)
:}
So the x intercepts are (-2) and (-4)
2. What is the vertex of this equation?
We can convert this equation into vertex form: F(x)=(x-color(red)a)^2+color(blue)b with vertex at (color(red)a,color(blue)b)
color(white)("XXX")F(x)
color(white)("XXXXX")=x^2+6x+8
color(white)("XXXXX")=x^2+6x+9-1
color(white)("XXXXX")=(x+3)^2-1
color(white)("XXXXX")=(x-color(red)((-3)))^2+color(blue)((-1))
which is the vertex form with vertex at (color(red)((-3)),color(blue)((-1)))
3. Draw the graph of this equation
graph{x^2+6x+8 [-8.836, 2.266, -1.523, 4.024]}
