SOLUTION: Would anyone be willing to help with these two problems. first reads. Graph the given relation by the table method. Determine whether the relation is a function. A. 2x-y=4 x= 0,2,

Algebra ->  Rational-functions -> SOLUTION: Would anyone be willing to help with these two problems. first reads. Graph the given relation by the table method. Determine whether the relation is a function. A. 2x-y=4 x= 0,2,      Log On


   

Question 160952: Would anyone be willing to help with these two problems. first reads. Graph the given relation by the table method. Determine whether the relation is a function. A. 2x-y=4 x= 0,2,4 y=____ . Second problem reads . Find the axis of symmetry and the vertex from each parabolic function. A. y=x^2-3x-5 ____ . These are the last of 72 questions I have done if anyone could help I would appreciate it thanks.
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
2x-y=4
When x=0 y=-4
when x=2 y=0
when x=4 y=4
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 2+x+%2B+-1+y+=+4 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-2%2F-1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 4/2 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/-1 = -4.
  • Slope is -2/-1 = 2.
  • Equation in slope-intercept form: y=2*x+-4.
graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+-4-8%2C+-4%2B8%2C+2%2Ax%2B-4+%29+

Yes the relation is a function
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%2B-5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A1%2A-5=29.

Discriminant d=29 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+29+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+29+%29%29%2F2%5C1+=+4.19258240356725
x%5B2%5D+=+%28-%28-3%29-sqrt%28+29+%29%29%2F2%5C1+=+-1.19258240356725

Quadratic expression 1x%5E2%2B-3x%2B-5 can be factored:
1x%5E2%2B-3x%2B-5+=+1%28x-4.19258240356725%29%2A%28x--1.19258240356725%29
Again, the answer is: 4.19258240356725, -1.19258240356725. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-5+%29


In order to find the vertex and axis of symmetry we need to transform the equation into standard form a(x-h)^2+k
The point (h,k) is the vertex and the line of symmetry is h
y=x^2-3x-5
The first step we need to do is complete the square since this is a problem that is not so easy to factor
divide the middle term by 2 and square the result. add the square term to the other side to maintain balance of the equation.

y+9/4=x^2-3x+9/4-5
than subtract 9/4 from both sides
y=x^2-3x+9/4(-9/4-20/4)
y=x^2-3x+9/4(-29/4)
y=(x-3/2)-29/4
the vertex is (3/2,-29/4)
The axis of symmetry is 3/2