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Rewriting Quadratics

9.9.4 Rewriting Quadratics

9.9.4 • Rewriting Quadratics

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For questions 1 – 2, use the function f(x)=x2f(x)=x2 that is shifted to create the function g(x)g(x) that has a vertex at (3,−2)(3,−2).

1.

Write g(x)g(x) in vertex form.

Compare your answer:

g(x)=(x−3)2−2g(x)=(x−3)2−2 The vertex form of a quadratic is f(x)=a(x−h)2+kf(x)=a(x−h)2+k. Since there is not a vertical stretch or compression or reflection mentioned, the vertex values are substituted for (h,k)(h,k). g(x)=(x−3)2+−2g(x)=(x−3)2+−2 becomes g(x)=(x−3)2−2g(x)=(x−3)2−2.

2.

Write g(x)g(x) in standard form.

Compare your answer: g(x)=x2−6x+7g(x)=x2−6x+7 g(x)=(x−3)2−2g(x)=(x−3)2−2 g(x)=(x−3)(x−3)−2g(x)=(x−3)(x−3)−2 g(x)=x2−3x−3x+9−2g(x)=x2−3x−3x+9−2 g(x)=x2−6x+7g(x)=x2−6x+7