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Parabolas quiz
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What is the standard form equation for a vertical parabola?
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What is the standard form equation for a vertical parabola?
The standard form is y = a(x-h)² + k.
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이 집합의 용어 (15)
하이드의 정의
What is the standard form equation for a vertical parabola?
The standard form is y = a(x-h)² + k.
How does the sign of 'a' affect the direction a vertical parabola opens?
If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.
Where is the vertex located in the equation y = a(x-h)² + k?
The vertex is at the point (h, k).
What is the axis of symmetry for a vertical parabola?
The axis of symmetry is x = h.
What is the standard form equation for a horizontal parabola?
The standard form is x = a(y-k)² + h.
How does the sign of 'a' affect the direction a horizontal parabola opens?
If 'a' is positive, the parabola opens to the right; if 'a' is negative, it opens to the left.
Where is the vertex located in the equation x = a(y-k)² + h?
The vertex is at the point (h, k).
What is the axis of symmetry for a horizontal parabola?
The axis of symmetry is y = k.
What is a parabola in terms of conic sections?
A parabola is a conic section defined as all points equidistant from a fixed line (directrix) and a fixed point (focus).
Where is the directrix located relative to the parabola?
The directrix is always outside the parabola.
Where is the focus located relative to the parabola?
The focus is always inside the parabola, in the direction it opens.
How do you switch from a vertical to a horizontal parabola equation?
Switch the roles of x and y, and also switch h and k in the equation.
What does the axis of symmetry represent in a parabola?
It is a line that divides the parabola into two mirror-image halves.
What is the relationship between any point on a parabola, the directrix, and the focus?
Any point on the parabola is the same distance from the directrix as it is from the focus.
Why is it important to recognize the vocabulary of directrix and focus?
Understanding these terms helps identify and describe parabolas as conic sections.