Question 4:
2x + 3y = 17 -- equation 1
5x + 6y = 32 -- equation 2
(equation 1) * 2
4x + 6y = 34 -- equation 3
(equation 2) - (equation 3)
x = -2 -- equation 4
plug (equation 4)'s value of x into (equation 1)
2(-2) + 3y = 17
3y - 4 = 17
3y = 21
y = 7
Thus the answer is x = -2 and y = 7
Question 5:
The vertex form of a quadrilateral looks like this:
[tex]y = a(x-h)^2 + k[/tex]
- a : coefficient of [tex]x^2\\[/tex]
- (h,k): coordinate of the vertex.
The x-coordinate of the vertex is equal to '-b/2a'. Where b is the
coefficient of x, so:
[tex]h = -\frac{b}{2a} =-\frac{-8}{2*1} =4[/tex]
There is also another formula to find the y-value of the vertex
coordinate, but the easier way to find it is to plug it into the original
equation:
[tex]k=(4)^2-8(4) + 12= 16 -32 + 12 = -16 + 12 = -4[/tex]
Since we know now that h = 4 and k = -4 and that a = 1, lets plug it into
the original equation.
[tex]y = 1*(x-4)^2 - 4 =(x^2-4)-4[/tex]
Thus the answer is [tex]y = (x-4)^2 -4[/tex]
Hope that helps!
