Section D Section D Checkpoint

Problem 1

For each pair of functions, describe how the graphs are different.

  1. f(x)=x2+3f(x) = x^2 + 3 and g(x)=-x2+3g(x) = \text{-}x^2 +3
  2. h(x)=x2+6h(x) = x^2 + 6 and j(x)=x2+1j(x) = x^2 + 1
  3. m(x)=x2+1m(x) = x^2 + 1 and p(x)=(x−2)2+1p(x) = (x-2)^2 + 1
  4. r(x)=x2r(x) = x^2 and s(x)=2x2s(x) = 2x^2
Show Solution
Solution
Sample responses:
  1. The graph of gg has the same shape as the graph of ff, but is flipped to open downward.
  2. The graph of jj has the same shape as the graph of hh, but is shifted 5 units down.
  3. The graph of pp has the same shape as the graph of mm, but the graph of pp is 2 units to the right.
  4. The graph of ss is taller and narrower than the graph of rr.
Show Sample Response
Sample Response
Sample responses:
  1. The graph of gg has the same shape as the graph of ff, but is flipped to open downward.
  2. The graph of jj has the same shape as the graph of hh, but is shifted 5 units down.
  3. The graph of pp has the same shape as the graph of mm, but the graph of pp is 2 units to the right.
  4. The graph of ss is taller and narrower than the graph of rr.

Problem 2

For each function, find the vertex, and then state whether it is a maximum or minimum.

  1. A(x)=-(x−3)2+2A(x) = \text{-}(x-3)^2 + 2
  2. B(x)=2(x+1)2+3B(x) = 2(x+1)^2 + 3
  3. C(x)=-5(x+2)2C(x) = \text{-}5(x+2)^2
  4. D(x)=x2−8D(x) = x^2 - 8
Show Solution
Solution
  1. (3,2)(3,2) maximum
  2. (-1,3)(\text{-}1,3) minimum
  3. (-2,0)(\text{-}2,0) maximum
  4. (0,-8)(0,\text{-}8) minimum
Show Sample Response
Sample Response
  1. (3,2)(3,2) maximum
  2. (-1,3)(\text{-}1,3) minimum
  3. (-2,0)(\text{-}2,0) maximum
  4. (0,-8)(0,\text{-}8) minimum