Question 1071426
here's your graph.


<img src = "http://theo.x10hosting.com/2017/030502.jpg" alt="$$$" </>


your axis of symmetry is x = 1.25


your vertex is (1.25, -2.875).


your y-intercept is y = -6.


there is no x-intercept.


your equation is:
&#8722;2x^2 + 5x &#8722; 6


since your equation is in standard quadratic equation form of:
ax^2 + bx + c = 0, you get:


a = -2
b = 5
c = -6


you can solve for the vertex using the formula x = -b/2a.
you will get x = -5/-4 = 1.25
you then solve for y by replacing x in the equation with 1.25 to get:
-2*(1.25)^2 + 5*(1.25) - 6 which is equal to -2.875.
your vertex is (1.25,-2.875).


your axis of symmetry is the vertical line through the vertex.
your axis of symmetry is therefore x = 1.25


you solve for the y-intercept by setting x = 0.
you will get y = -2x^2 + 5x - 6 becomes y = -2*0 + 5*0 - 6 which becomes y = -6.


you would factor the quadratic equation to find the x-intercepts.
you will get complex roots which tells you that there is no x-intercept.
you would use the quadratic formula.
when you do, you will get:
1.25 + 1.1989578808282i
1.25 - 1.1989578808282i
It has Complex Roots !
i used an online quadratic equation solver to get these results.
a picture of the results of the use of that solver are shown below:


<img src ="http://theo.x10hosting.com/2017/030503.jpg" alt="$$$" </>


i could have done it manually and would have gotten the same results.
the quadratic formula is:
<pre>


                   -b plus or minus sqrt(b^2 - 4ac)
            x =    --------------------------------
                               2a
</pre>


you would replace a with -2, b with 5 and c with -6 and solve.


you would get the same answer that the solver is showing you.


the preliminary results would be x = 5/4 plus or minus sqrt(-23)/4.


negative square root indicates complex root.


you would then take the next step to get x = 5/4 plus or minus sqwt(23)/4 * i.


resolve that and you get what the solver is showing you.,


complex roots means the graph is not crossing the x-axis which means you have no x-intercepts.