### About Graphing Parabolas:

When we graph a parabola, we are generally concerned with three things. First and foremost, we look for the vertex. This is the highest or lowest point, depending on whether the parabola faces up or down. Secondly, we are looking at the horizontal shift or movement along the x axis. Lastly, we are looking at the vertical shift, or movement along the y axis.

Test Objectives

- Demonstrate the ability to find the vertex of a parabola
- Demonstrate the ability to find the horizontal shift
- Demonstrate the ability to find the vertical shift

#1:

Instructions: Identify the vertex of each parabola.

a) $$f(x) = -\frac{1}{5}x^2$$

b) $$f(x) = (x - 3)^2 + 5$$

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#2:

Instructions: Identify the vertex of each parabola.

a) $$f(x) = (x + 9)^2$$

b) $$f(x) = (x - 13)^2 + 4$$

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#3:

Instructions: State the horizontal and/or vertical shift for each parabola when compared to f(x) = x^{2}.

a) $$f(x) = (x- 19)^2$$

b) $$f(x) = x^2 - 5$$

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#4:

Instructions: State the horizontal and/or vertical shift for each parabola when compared to f(x) = x^{2}.

a) $$f(x) = (x + 2)^2 - 14$$

b) $$f(x) = (x - 7)^2 + 7$$

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#5:

Instructions: State the horizontal and/or vertical shift for each parabola when compared to f(x) = x^{2}.

a) $$f(x) = (x - 17)^2 - 12$$

b) $$f(x) = (x + 1)^2 - 23$$

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Written Solutions:

#1:

Solutions:

a) $$vertex: (0,0)$$

b) $$vertex: (3,5)$$

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#2:

Solutions:

a) $$vertex: (-9,0)$$

b) $$vertex: (13,4)$$

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#3:

Solutions:

a) $$shifts \hspace{.25em} 19\hspace{.25em} units\hspace{.25em} right$$

b) $$shifts\hspace{.25em} 5 \hspace{.25em}units\hspace{.25em} down$$

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#4:

Solutions:

a) $$shifts \hspace{.25em} 2\hspace{.25em} units\hspace{.25em} left ,\hspace{.25em} 14 \hspace{.25em} units \hspace{.25em} down$$

b) $$shifts \hspace{.25em} 7\hspace{.25em} units\hspace{.25em} right,\hspace{.25em} 7 \hspace{.25em} units \hspace{.25em} up$$

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#5:

Solutions:

a) $$shifts \hspace{.25em}17\hspace{.25em} units\hspace{.25em} right ,\hspace{.25em} 12 \hspace{.25em} units \hspace{.25em} down$$

b) $$shifts \hspace{.25em} 1\hspace{.25em} unit\hspace{.25em} left,\hspace{.25em} 23 \hspace{.25em} units \hspace{.25em} down$$