About Graphing Horizontal Parabolas:
Horizontal parabolas are of the form: x = a(y - k)2 + h or x = ay2 + by + c. We approach graphing a horizontal parabola in the same way that we graph a vertical parabola. First, we place our equation in vertex form. Once this is done, we can plot the vertex and use the step pattern to find additional points. We will then reflect across the line y = k to find points on the other side of our parabola. Lastly, we will sketch our graph by drawing a smooth curve through the points.
Test Objectives
- Demonstrate the ability to write a horizontal parabola in vertex form
- Demonstrate the ability to sketch the graph of a horizontal parabola
#1:
Instructions: Find the vertex form, axis of symmetry, and sketch the graph of each.
$$a)\hspace{.2em}x=-3y^2 - 6y + 1$$
$$b)\hspace{.2em}x=y^2 - 6y + 12$$
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#2:
Instructions: Find the vertex form, axis of symmetry, and sketch the graph of each.
$$a)\hspace{.2em}x=-2y^2 - 20y - 47$$
$$b)\hspace{.2em}x=-y^2 + 6y - 10$$
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#3:
Instructions: Find the vertex form, axis of symmetry, and sketch the graph of each.
$$a)\hspace{.2em}x=-\frac{1}{2}y^2 - 4y - 10$$
$$b)\hspace{.2em}x=-y^2 + 10y - 23$$
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#4:
Instructions: Find the vertex form, axis of symmetry, and sketch the graph of each.
$$a)\hspace{.2em}x=3y^2 + 6y - 4$$
$$b)\hspace{.2em}x=2y^2 + 8y + 5$$
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#5:
Instructions: Find the vertex form, axis of symmetry, and sketch the graph of each.
$$a)\hspace{.2em}x=2y^2 + 12y + 22$$
$$b)\hspace{.2em}x=\frac{1}{4}y^2 - \frac{1}{2}y + \frac{5}{4}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}$$ Vertex Form: $$x = -3(y + 1)^2 + 4$$ Axis of Symmetry: $$y = -1$$
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$$b)\hspace{.2em}$$ Vertex Form: $$x = (y - 3)^2 + 3$$ Axis of Symmetry: $$y = 3$$
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#2:
Solutions:
$$a)\hspace{.2em}$$ Vertex Form: $$x = -2(y + 5)^2 + 3$$ Axis of Symmetry: $$y = -5$$
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$$b)\hspace{.2em}$$ Vertex Form: $$x = -(y - 3)^2 - 1$$ Axis of Symmetry: $$y = 3$$
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#3:
Solutions:
$$a)\hspace{.2em}$$ Vertex Form: $$x = -\frac{1}{2}(y + 4)^2 - 2$$ Axis of Symmetry: $$y = -4$$
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$$b)\hspace{.2em}$$ Vertex Form: $$x = -(y - 5)^2 + 2$$ Axis of Symmetry: $$y = 5$$
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#4:
Solutions:
$$a)\hspace{.2em}$$ Vertex Form: $$x = 3(y + 1)^2 - 7$$ Axis of Symmetry: $$y = -1$$
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$$b)\hspace{.2em}$$ Vertex Form: $$x = 2(y + 2)^2 - 3$$ Axis of Symmetry: $$y = -2$$
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#5:
Solutions:
$$a)\hspace{.2em}$$ Vertex Form: $$x = 2(y + 3)^2 + 4$$ Axis of Symmetry: $$y = -3$$
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$$b)\hspace{.2em}$$ Vertex Form: $$x = \frac{1}{4}(y - 1)^2 + 1$$ Axis of Symmetry: $$y = 1$$
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