MATH SOLVE

3 months ago

Q:
# The vertex of a parabola is at (1 , 3), and its focus is at (1 , 3.5). Which function does the graph with these attributes represent?

Accepted Solution

A:

ANSWER[tex]y = 2{(x - 1)}^{2} + 3[/tex]EXPLANATIONThe vertex of the given parabola is;[tex](h,k)=(1,3)[/tex]and the focus is[tex](1,3.5)[/tex]The given parabola has the line of symmetry parallel to the y-axis.It's equation is given by;[tex](y - k) = 4p {(x - h)}^{2} [/tex][tex] |p| = 0.5[/tex]The distance from the focus to the vertex.[tex]p = 0.5[/tex]The parabola will open up because the directrix is [tex]y = 2.5[/tex]The equation of the parabola is [tex](y - 3) = 4 \times 0.5{(x - 1)}^{2} [/tex]Or[tex]y = 2{(x - 1)}^{2} + 3[/tex]