Question 164513
{{{y=(x+3)(x-5)}}} Start with the given equation



{{{y=x^2-5x+3x-15}}} FOIL



{{{y=x^2-2x-15}}} Combine like terms.



In order to find the vertex, we first need to find the x-coordinate of the vertex.



To find the x-coordinate of the vertex, use this formula: {{{x=(-b)/(2a)}}}.



{{{x=(-b)/(2a)}}} Start with the given formula.



From {{{y=x^2-2x-15}}}, we can see that {{{a=1}}}, {{{b=-2}}}, and {{{c=-15}}}.



{{{x=(-(-2))/(2(1))}}} Plug in {{{a=1}}} and {{{b=-2}}}.



{{{x=(2)/(2(1))}}} Negate {{{-2}}} to get {{{2}}}.



{{{x=(2)/(2)}}} Multiply 2 and {{{1}}} to get {{{2}}}.



{{{x=1}}} Divide.



So the x-coordinate of the vertex is {{{x=1}}}. Note: this means that the axis of symmetry is also {{{x=1}}}.



Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.



{{{y=x^2-2x-15}}} Start with the given equation.



{{{y=(1)^2-2(1)-15}}} Plug in {{{x=1}}}.



{{{y=1(1)-2(1)-15}}} Square {{{1}}} to get {{{1}}}.



{{{y=1-2(1)-15}}} Multiply {{{1}}} and {{{1}}} to get {{{1}}}.



{{{y=1-2-15}}} Multiply {{{-2}}} and {{{1}}} to get {{{-2}}}.



{{{y=-16}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=-16}}}.



So the vertex is *[Tex \LARGE \left(1,-16\right)].