Answer:
Explanation:
The quadratic equation is given as:
```
y = 20x^2 + 180x - 567
```
To find the roots of the quadratic, we can use the quadratic formula:
```
x = (-b ± √(b^2 - 4ac)) / 2a
```
In this case, the coefficients are:
```
a = 20
b = 180
c = -567
```
Substituting these values into the quadratic formula, we get:
```
x = (-180 ± √(180^2 - 4 * 20 * -567)) / 2 * 20
```
```
x = (-180 ± √(32400 + 42680)) / 40
```
```
x = (-180 ± √75080) / 40
```
```
x = (-180 ± 274.16) / 40
```
```
x = -4.25, -14.25
```
Therefore, the roots of the quadratic are -4.25 and -14.25.
To find the vertex of the quadratic, we can use the formula:
```
(-b / 2a, (4ac - b^2) / 4a)
```
In this case, the vertex is:
```
(-180 / 2 * 20, (4 * 20 * -567 - 180^2) / 4 * 20)
```
```
(-4.5, -79.75)
```
Therefore, the vertex of the quadratic is at (-4.5, -79.75).
The roots and the vertex of the quadratic are rounded to 3 decimal places.