Which equation has a graph that is a parabola with a vertex at (5, 3)?

a. y = (x – 5)2 + 3
b. y = (x + 5)2 + 3
c. y = (x – 3)2 + 5
d. y = (x + 3)2 + 5

we know that

The vertex form of a quadratic equation is equal to

where

(h,k) is the vertex of the parabola

Let's analyze each case to determine the solution

case a)

in this problem

using a graph tool

see the attached figure N

case b)

in this problem

using a graph tool

see the attached figure N

case c)

in this problem

using a graph tool

see the attached figure N

case d)

in this problem

using a graph tool

see the attached figure N

therefore

the answer is

The equation that has a graph that is a parabola with a vertex at is

case a)

she will travel a distance in the range of 3 - 11 miles