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Parabolas Solutions

A parabola is a type of conic section that only slices through one cone.
The parent equation, either $y = x^{2}$ or $x = y^{2}$ , determines many things, primarily the direction of the opening of the parabola.
You need to identify the direction in which the parabola opens (up/down, right/left) before graphing or writing equations in vertex form.
The variable that is raised to the second power will determine the direction of the parabola and whether the equation in standard form will start with x or y.

Parabola Parent Graph Form	$y = x^{2}$	$x = y^{2}$
Sketch
Vertex Form	$y = a {(x - h)}^{2} + k$	$x = a {(y - k)}^{2} + h$
Direction of Opening	Up when $a > 0$ Down when	Right when $a > 0$ Left when $a < 0$
Vertex	(h, k)	(h, k)
Axis of Symmetry	*x = h*	*y = k*
VLT	Yes, this parabola is a function.	No, this parabola is not a function.
HLT	No, the inverse is not a function.	Yes, the inverse is a function.

Graph.

$x = {(y - 3)}^{2} - 4$

Plan
Steps to graph parabolas in vertex form

Implement

$a = 1, h = - 4, k = 3$

Opens right (a is positive) ↪ $x = y^{2}$

Note

You can include the horizontal axis of symmetry as a dashed line if you need a visual to create a symmetric graph.

Remember that when a parabola opens right/left, k is inside the parentheses.

You have graphed many quadratic functions in vertex form in Lessons 17 and 18. Refer to those lessons as needed to review graphing parabolas.