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,

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) (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 describes a sloping line. For any
equation ax+by+c = 0, slope is .

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.

Yes the relation is a function

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=29 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4.19258240356725, -1.19258240356725. Here's your graph:

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

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