For each function below: (1) Draw a neat sketch graph indicating the coordinates of the intercepts with the axes, the coordinates of the turning point and the equation of the axis of symmetry. (2) Determine the domain and range. (3) Determine the values of x for which the graph increases and decreases. (4) Determine the maximum or minimum value of the graph. (a) f(x)=(x+1)^{2}-4 (b) f(x)=-(x+1)^{2}+4 (c) f(x)=(x-1)^{2}-4 (d) f(x)=-(x-1)^{2}+4 (e) f(x)=(x-2)^{2}-1 (f) g(x)=(x+1)^{2}+2 (g) g(x)=-(x+1)^{2}-2 (h) g(x)=(x-2)^{2}-9 (i) g(x)=2(x+1)^{2}-2 (j) g(x)=(x-4)^{2}-2

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For each function, sketch the graph showing intercepts, turning point, and axis of symmetry. Determine the domain and range. Identify where the graph increases and decreases, and find the maximum or minimum value. Function (a): $$ f(x) = (x+1)^2 - 4 $$ - Vertex at $$ x = -1 $$, $$ f(-1) = -4 $$ - Axis of symmetry: $$ x = -1 $$ - Increases for $$ x > -1 $$, decreases for $$ x < -1 $$ - Minimum value: $$ -4 $$ Function (b): $$ f(x) = -(x+1)^2 + 4 $$ - Vertex at $$ x = -1 $$, $$ f(-1) = 4 $$ - Axis of symmetry: $$ x = -1 $$ - Decreases for $$ x > -1 $$, increases for $$ x < -1 $$ - Maximum value: $$ 4 $$ Function (c): $$ f(x) = (x-1)^2 - 4 $$ - Vertex at $$ x = 1 $$, $$ f(1) = -4 $$ - Axis of symmetry: $$ x = 1 $$ - Increases for $$ x > 1 $$, decreases for $$ x < 1 $$ - Minimum value: $$ -4 $$ Function (d): $$ f(x) = -(x-1)^2 + 4 $$ - Vertex at $$ x = 1 $$, $$ f(1) = 4 $$ - Axis of symmetry: $$ x = 1 $$ - Decreases for $$ x > 1 $$, increases for $$ x < 1 $$ - Maximum value: $$ 4 $$ Function (e): $$ f(x) = (x-2)^2 - 1 $$ - Vertex at $$ x = 2 $$, $$ f(2) = -1 $$ - Axis of symmetry: $$ x = 2 $$ - Increases for $$ x > 2 $$, decreases for $$ x < 2 $$ - Minimum value: $$ -1 $$ Function (f): $$ g(x) = (x+1)^2 + 2 $$ - Vertex at $$ x = -1 $$, $$ g(-1) = 2 $$ - Axis of symmetry: $$ x = -1 $$ - Increases for all $$ x $$ - Minimum value: $$ 2 $$ Function (g): $$ g(x) = -(x+1)^2 - 2 $$ - Vertex at $$ x = -1 $$, $$ g(-1) = -2 $$ - Axis of symmetry: $$ x = -1 $$ - Decreases for all $$ x $$ - Maximum value: $$ -2 $$ Function (h): $$ g(x) = (x-2)^2 - 9 $$ - Vertex at $$ x = 2 $$, $$ g(2) = -9 $$ - Axis of symmetry: $$ x = 2 $$ - Increases for $$ x > 2 $$, decreases for $$ x < 2 $$ - Minimum value: $$ -9 $$ Function (i): $$ g(x) = 2(x+1)^2 - 2 $$ - Vertex at $$ x = -1 $$, $$ g(-1) = -2 $$ - Axis of symmetry: $$ x = -1 $$ - Increases for all $$ x $$ - Minimum value: $$ -2 $$ Function (j): $$ g(x) = (x-4)^2 - 2 $$ - Vertex at $$ x = 4 $$, $$ g(4) = -2 $$ - Axis of symmetry: $$ x = 4 $$ - Increases for $$ x > 4 $$, decreases for $$ x < 4 $$ - Minimum value: $$ -2 $$

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