Answer:
Here's what I get
Step-by-step explanation:
The formula for a quadratic equation is
ax² + bx + c = 0
The quadratic formula gives the roots:
![x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%3D%20%20%5Cdfrac%7B-b%5Cpm%5Csqrt%7BD%7D%7D%7B2a%7D)
D is the discriminant.
It tells us the number of roots to the equation — the number of times the graph crosses the x-axis.
![D = \begin{cases}\text{positive} & \quad \text{2 real solutions}\\\text{zero} & \quad \text{1 real solution}\\\text{negative} & \quad \text{0 real solutions}\\\end{cases}](https://tex.z-dn.net/?f=D%20%3D%20%5Cbegin%7Bcases%7D%5Ctext%7Bpositive%7D%20%20%26%20%5Cquad%20%5Ctext%7B2%20real%20solutions%7D%5C%5C%5Ctext%7Bzero%7D%20%26%20%5Cquad%20%5Ctext%7B1%20real%20solution%7D%5C%5C%5Ctext%7Bnegative%7D%20%26%20%5Cquad%20%5Ctext%7B0%20real%20solutions%7D%5C%5C%5Cend%7Bcases%7D)
It doesn't matter if the graph opens upwards or downwards.
If D > 0, the graph crosses the x-axis at two points.
If D = 0, the graph touches the x-axis at one point.
If D < 0, the graph never reaches the x-axis.
Your graph must look like one of the two graphs on the right in the Figure below.