(x-11)2=2 Two solution
Step-by-step explanation:
Step by step solution :
Step 1 :
1.1 Evaluate : (x-11)2 = x2-22x+121
Trying to factor by splitting the middle term
1.2 Factoring x2-22x+119
The first term is, x2 its coefficient is 1 .
The middle term is, -22x its coefficient is -22 .
The last term, "the constant", is +119
Step-1 : Multiply the coefficient of the first term by the constant 1 • 119 = 119
Step-2 : Find two factors of 119 whose sum equals the coefficient of the middle term, which is -22 .
-119 + -1 = -120
-17 + -7 = -24
-7 + -17 = -24
-1 + -119 = -120
1 + 119 = 120
7 + 17 = 24
17 + 7 = 24
119 + 1 = 120
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 22x + 119 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-22x+119
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 11.0000
Plugging into the parabola formula 11.0000 for x we can calculate the y -coordinate :
y = 1.0 * 11.00 * 11.00 - 22.0 * 11.00 + 119.0
or y = -2.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-22x+119
Axis of Symmetry (dashed) {x}={11.00}
Vertex at {x,y} = {11.00,-2.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 9.59, 0.00}
Root 2 at {x,y} = {12.41, 0.00}
