Function Transformations Review

Match each of the transformations with the following variations of $$f\left(x\right)$$ .

Given the black graph $$f\left(x\right)$$ , plot the graph of the transformed function $$f\left(\frac{1}{3}x\right)$$ .

Given the black graph $$f\left(x\right)$$ , plot the graph of the transformed function $$\frac{1}{2}f\left(x\right)$$ .

Given the black graph $$f\left(x\right)$$ , plot the graph of the transformed function $$f\left(x+4\right)-6$$ .

Given the black graph $$f\left(x\right)$$ , plot the graph of the transformed function $$-f\left(x\right)$$ .

The vertex of the parabola with equation $$y=\ -2\left(x-3\right)^2+5$$

(a)  

Answer the following question by completing the square or using the axis of symmetry:

The vertex of the parabola $$y=x^2-8x+15$$ is

(a)  

Bozo attempts to complete the square on a quadratic. Identify the line that contains the initial mistake:
$$y=2x^2-4x-48$$

Line 1: $$\frac{y}{2}=x^2-2x-24$$

Line 2: $$\frac{y}{2}+1=x^2-2x+1-24$$

Line 3: $$\frac{y}{2}+1=\left(x+1\right)^2-24$$

Line 4: $$\frac{y}{2}=\left(x+1\right)^2-25$$

Line 5: $$y=2\left(x+1\right)^2-50$$

Match each feature of the parabola $$y=ax^2+bx+c$$ with the correct procedures to find them.