Question

X^2+17x+50=0 to the nearest tenth.

Answer 1

Answer: 2.1      Find the Vertex of   y = x2-17x-50

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.  

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.  

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   8.5000  

Plugging into the parabola formula   8.5000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 - 50.0

or   y = -122.250

Step-by-step explanation:

Answer 2

Since you cannot really factor this problem easily, we are going to resort to the quadratic formula!

x= -b+or- sqrt(b^2-4ac)    / 2a

x=-17+ or - sqrt(17^2-4*50)   /2

x=-17+ or - sqrt89 /2

Now we just need estimate sqrt 89 which is about 9.43 and I will not bother to show the step I did to estimate its about 9.43.

So x= -17+ or -9.43 /2

x= -26.43/2 or -7.57/2

x=-13.215 or -3.785

Round to nearest tenth digit.

x= -13.2 or -3.8

Hope this helps any questions just ask in the comments.