Respuesta :
Answer:
Similarity: Both functions has same vertex at point [tex](-3,2)[/tex].
Difference: [tex]f(x)=-2(x+3)^2+2[/tex] is downward opening parabola, while [tex]g(x)=5(x+3)^2+2[/tex] is an upward opening parabola.
Step-by-step explanation:
We have been given two functions as: [tex]f(x)=-2(x+3)^2+2[/tex] and [tex]g(x)=5(x+3)^2+2[/tex]. We are asked to compare the graphs of the given function.
We know that standard form of a parabola with vertex at point (h,k) is in format [tex]y=a(x-h)^2+k[/tex].
Let us find the similarity in both graphs.
- Upon comparing both functions with standard form of a parabola, we can see that vertex of the both parabolas is at point [tex](-3,2)[/tex].
Let us find the difference in both graphs.
We can see that leading coefficient of [tex]g(x)=5(x+3)^2+2[/tex] is positive, so it will be an upward opening parabola.
We can also see that leading coefficient of [tex]f(x)=-2(x+3)^2+2[/tex] is negative, so it will be a downward opening parabola.
