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siniylev [52]
3 years ago
14

The first three steps in determining the solution set of the system of equations, y = –x2 – 2x + 8 and y = 2x + 11, algebraicall

y are shown in the table
Mathematics
1 answer:
shutvik [7]3 years ago
5 0
First step
Using substitution you can fill 2x + 11 in for the y part of the first equation
This will look like: 2x + 11 = -x^2 -2x + 8

Second step
Now we need to solve for the variable by combining like terms you can start by adding x^2 + 2x -8 to both sides
You get 0 = x^2 +4x +3

Third step
Factor
(X+3)(x+1)=0

If you need the y values you can fill in x= -3 to the second equation y= 2(-3) + 11 and y=5
First point is (-3,5)

The other point is found by filling x=-1 into the second equation: y= 2(-1) +11 and y = 9
Second point is (-1,9)
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Answer:

The equation of the parabola is y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4, whose real vertex is (x,y) = (2, -5.333), not (x,y) = (2, -5).

Step-by-step explanation:

A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:

(x_{1}, y_{1}) = (-2, 0), (x_{2}, y_{2}) = (6, 0), (x_{3}, y_{3}) = (0, -4)

From definition of second order polynomial and the three points described above, we have the following system of linear equations:

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The solution of this system is: a = \frac{1}{3}, b = - \frac{4}{3}, c = -4. Hence, the equation of the parabola is y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4. Lastly, we must check if (x,y) = (2, -5) belongs to the function. If we know that x = 2, then the value of y is:

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(x,y) = (2, -5) does not belong to the function, the real point is (x,y) = (2, -5.333).

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