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PLEASE HELP ASAP - ILL GIVE BRAINLIEST

PLEASE HELP ASAP ILL GIVE BRAINLIEST class=

Sagot :

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]