Answer:
Listed below
Explanation:
This is a cuadratic function excercise.
We know that cuadratic functions have the following formula:

The graphic of this function will give us a parabola, that can be graphed knowing four points: the two or less x-intercepts, the y-intercept, and the vertex (Xv;Yv).
A) The vertex
The vertex is a point on the graph, so we have to know it's value on the X axis and on the Y axis.
To know the value of Xv we can calculate it using the following formula:

We know that in this case:

So we supplant said values on the formula and we get:

To know the value of Yv, we suppland the value of Xv on the function's formula.

So we know now that
and

b) The y-intercept is the value of C on the function's formula. We know that c=-6, so

c) The x-intercepts can be resolved using the following formula:
![x=\frac{-b+-\sqrt[2]{b^(2)-4ac} }{2a} \\\\x=\frac{-5+-\sqrt[2]{(-5)^(2)-4.1.(-6)} }{2.1} \\x=\frac{-(-5)+-\sqrt[2]{25+24} }{2}\\x=\frac{5+-\sqrt[2]{49} }{2.1}\\x=(5+-7 )/(2.1)](https://img.qammunity.org/2020/formulas/mathematics/high-school/eoh1l3ja6q3lxqzlq1kfg39d5cfnxhdciy.png)
This means that this formula can have two posisible solutions:

Or:

So that are the X-intercepts: x=6 and x=-1