Table of Contents
How do you describe a parabola?
A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ), and. a fixed straight line (the directrix )
What is the symmetry of a parabola?
The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
What is the vertex turning point of the parabola?
If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.
Which best describes the vertex of a parabola?
Characteristics of Parabolas | Other Quiz – Quizizz. Q. Which best describes the vertex of a parabola? Any point on the parabola.
How do you find the turning point?
The easiest way to find the turning point is when the quadratic is in turning point form (y = a(x – h)2 + k), where (h, k) is the turning point….From the graph above we can see that:
- When a > 0 (positive) the parabola is concave up.
- When a < 0 (negative) the parabola is concave down.
What is parabola in projectile motion?
Projectile motion is parabolic because the vertical position of the object is influenced only by a constant acceleration, (if constant drag etc. is also assumed) and also because horizontal velocity is generally constant.
What is parabola in calculus?
Parabola. A parabola is the set of points that are equidistant from a fixed point on the interior of the curve, called the ”’focus”’, and a line on the exterior, called the ”’directrix”’. The directrix is vertical or horizontal, depending on the orientation of the parabola.
How do you compare the distance from the focus to any point on the parabola to the distance from the same point to the Directrix?
From the definition of a parabola, the distance from any point on the parabola to the focus is equal to the distance from that same point to the directrix. Therefore, by definition, the eccentricity of a parabola must be 1 .
Where is the vertex in an equation?
Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the “vertex”. If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k).
What is the equation of the axis of symmetry of the parabola?
The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y = a x 2 + b x + c , the axis of symmetry is a vertical line x = − b 2 a .
How do you find the vertex of a parabola?
Knowing the axis of symmetry is not enough to determine the vertex. The axis of symmetry contains infinitely many point, one of which is the vertex of the parabola. Without more information it is impossible to determine which of those infinitely many points is the vertex.
How do you find the y intercept of a parabola?
Given a parabola y = a x 2 + b x + c, the point at which it cuts the y -axis is known as the y -intercept. The y -intercept will always have coordinates: (0, c) where c is the only term in the parabola ‘s equation without an x.
What is concave-down parabola?
Concave-Down Parabola, “unhappy parabola”. Given a parabola y = a x 2 + b x + c, the point at which it cuts the y -axis is known as the y -intercept . where c is the only term in the parabola ‘s equation without an x .