<span><span>y=−<span>x2</span>+2x−7</span><span>y=-<span>x2</span>+2x-7</span></span>Complete the square on the right side of the equation.Tap for more steps...<span><span>−<span><span>(x−1)</span>2</span>−6</span><span>-<span><span>(x-1)</span>2</span>-6</span></span>Reorder the right side of the equation to match the vertex form of a parabola.<span><span>y=−<span><span>(x−1)</span>2</span>−6</span><span>y=-<span><span>(x-1)</span>2</span>-6</span></span>Use the vertex form, <span><span>y=a<span><span>(x−h)</span>2</span>+k</span><span>y=a<span><span>(x-h)</span>2</span>+k</span></span>, to determine the values of <span>aa</span>, <span>hh</span>, and <span>kk</span>.<span><span>a=−1</span><span>a=-1</span></span><span><span>h=1</span><span>h=1</span></span><span><span>k=−6</span><span>k=-6</span></span>Find the vertex <span><span>(h,k)</span><span>(h,k)</span></span>.<span><span>(1,−6)</span><span>(1,-6)</span></span>
A student draws a geometric shape where all of the sides are different lengths. which of the following geometric shapes could the student have drawn?
a. rhombus
First find the slope between any two points:

Where

are the two points
So calculating the slope:

So the slope is

And our equation will be in the format of

where

and

So, now we have half of the equation:

Now to calculate b, we can plug in a point

and solve for b.
So

Lets use the point

So:

And then:

So our final equation is