# Which function has a range of vy s 5)? of(x) = (x - 4)2 + 5 O (x) = -(x - 4)2 + 5 o f(x) = (x - 5)2 + 4 Of(x) = -(x - 5)2 + 4

###### Question:

of(x) = (x - 4)2 + 5

O (x) = -(x - 4)2 + 5

o f(x) = (x - 5)2 + 4

Of(x) = -(x - 5)2 + 4

## Answers

Answer:see the explanationStep-by-step explanation:Verify the range of each quadratic functioncase 1) we have[tex]f(x)=(x-4)^2+5[/tex]This is a vertical parabola open upward (the leading coefficient is positive)The function is written in vertex formThe vertex represent a minimumThe vertex is the point (4,5)The range is the interval [5,∞)[tex]y\geq 5[/tex]case 2) we have[tex]f(x)=-(x-4)^2+5[/tex]This is a vertical parabola open downward (the leading coefficient is negative)The function is written in vertex formThe vertex represent a maximumThe vertex is the point (4,5)The range is the interval (-∞,5][tex]y\leq 5[/tex]case 3) we have[tex]f(x)=(x-5)^2+4[/tex]This is a vertical parabola open upward (the leading coefficient is positive)The function is written in vertex formThe vertex represent a minimumThe vertex is the point (5,4)The range is the interval [4,∞)[tex]y\geq 4[/tex]case 4) we have[tex]f(x)=-(x-5)^2+4[/tex]This is a vertical parabola open downward (the leading coefficient is negative)The function is written in vertex formThe vertex represent a maximumThe vertex is the point (5,4)The range is the interval (-∞,4][tex]y\leq 4[/tex]