Determine the vertex of the following quadratic functions Ex

Determine the vertex of the following quadratic functions. Express your answer as an ordered pair in the form (a, ) a. g(z) (7a + 10)(z +9) Preview b)(z) = z2-62 Preview cp(r) -6 Preview

Solution

a)

g(x)=(7x+10)(x+9)

g(x)=7x²+73x+90

g(x)=7(x²+(73_/7)x)+90

g(x)=7(x²+(73_/7)x+(73_/14)²-(73_/14)²)+90

g(x)=7(x²+(73_/7)x+(73_/14)²)-7*(73_/14)²+90

g(x)=7(x+(73_/14))²  -(5329_/28)+90

g(x)=7(x-(-73_/14))²  -(2809_/28)

vertex is (-73_/14  ,-2809_/28)

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b)

j(x)=x²-6²

j(x)=x²-36

vertex is (0,-36)

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c)

p(x)=-3x²-2x+6

p(x)=-3(x²+(2_/3)x) +6

p(x)=-3(x²+(2_/3)x +(1_/3)²-(1_/3)²) +6

p(x)=-3(x²+(2_/3)x +(1_/3)²)+3(1_/3)² +6

p(x)=-3(x+(1_/3))² + (1_/3) +6

p(x)=-3(x-(-1_/3))² + (19_/3)

vertex is (-1_/3,19_/3)