Question 151429

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)}}}.

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

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

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

So the x-coordinate of the vertex is {{{x=-1/2}}}. Note: this means that the axis of symmetry is also {{{x=-1/2}}}.

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

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

{{{y=1/4-1/2-2}}} Square {{{-1/2}}} to get {{{1/4}}}.

{{{y=1/4-2/4-2}}} Multiply {{{1/2}}} by {{{2/2}}} to get {{{2/4}}}.

{{{y=1/4-2/4-8/4}}} Multiply {{{2}}} by {{{4/4}}} to get {{{8/4}}}.

{{{y=-9/4}}} Combine the fractions.

So the y-coordinate of the vertex is {{{y=-9/4}}}.

So the vertex is *[Tex \LARGE \left(-\frac{1}{2},-\frac{9}{4}\right)] or *[Tex \LARGE \left(-0.5,-2.25\right)] in decimal form.