Respuesta :
Answer: 12*x-7-(13*(x-12)*x)=0
Step by Step Solution
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Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
12*x-7-(13*(x-12)*x)=0
Step by step solution :
STEP
1
:
Equation at the end of step 1
(12x - 7) - (13 • (x - 12) • x) = 0
STEP
2
:
Equation at the end of step 2
(12x - 7) - 13x • (x - 12) = 0
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
-13x2 + 168x - 7 = -1 • (13x2 - 168x + 7)
Trying to factor by splitting the middle term
4.2 Factoring 13x2 - 168x + 7
The first term is, 13x2 its coefficient is 13 .
The middle term is, -168x its coefficient is -168 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 13 • 7 = 91
Step-2 : Find two factors of 91 whose sum equals the coefficient of the middle term, which is -168 .
-91 + -1 = -92
-13 + -7 = -20
-7 + -13 = -20
-1 + -91 = -92
1 + 91 = 92
7 + 13 = 20
13 + 7 = 20
91 + 1 = 92
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
4
:
-13x2 + 168x - 7 = 0
STEP
5
:
Parabola, Finding the Vertex:
5.1 Find the Vertex of y = -13x2+168x-7
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens down and accordingly has a highest point (AKA absolute maximum) . We know this even before plotting "y" because the coefficient of the first term, -13 , is negative (smaller 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 6.4615
Plugging into the parabola formula 6.4615 for x we can calculate the y -coordinate :
y = -13.0 * 6.46 * 6.46 + 168.0 * 6.46 - 7.0
or y = 535.769
