Answer:
4) [tex]y=-\frac{1}{3} (x-2)^2-3[/tex] 7) [tex]2x^2+12x+18[/tex]
5) [tex](-2,-3)[/tex] 8) [tex](0,-3)[/tex]
Step-by-step explanation:
7) Add [tex]2y^2[/tex] to both sides of the equation.
[tex]x-12y-18=2y^2[/tex]
Add 12y to both sides of the equation.
[tex]x-18=2y^2+12y[/tex]
Add 18 to both sides of the equation.
[tex]x=2y^2+12y+18[/tex]
Use the form of [tex]ax^{2} +bx+c[/tex] to find the values of a, b, and c.
a = 2, b = 12, c = 18
Substitute the values of a and b into the formula [tex]d=\frac{b}{2a}[/tex]
[tex]d=\frac{12}{2(2)}[/tex]
Simplify the bottom.
d = 3
Find the value of e using the formula e = [tex]c-\frac{b^2}{4a}[/tex]
Raise 12 to the power of 2
[tex]e=18-\frac{144}{4(2)}[/tex]
Multiply 4 by 2.
[tex]e=18-\frac{144}{8}[/tex]
Divide 144 by 8.
[tex]e=18-1[/tex] · 18
Multiply [tex]-1[/tex] by 8.
[tex]e = 18-18[/tex]
Subtract 18 from 18.
e = 0
Substitute the values of a, d, and e into the vertex form [tex]a(x+d)^2+e[/tex].
[tex]2(y+3)^2+0[/tex]
Set x equal to the new right side.
[tex]x=2(y+3)^2+0[/tex]
Use the vertex form, [tex]x=a(y-k)^2+h[/tex], to determine the values of a h & k.
a = 2
h = 0
k = [tex]-3[/tex]
Find the vertex [tex](h,k)[/tex]
[tex](0,-3)[/tex]
