Flashcard 4.3 & 4.4

Front

What is the equation of the directrix for a parabola with a focus at (0,3) and a vertex at the origin?

Back

y = -3

Front

Write the equation of the quadratic function with x-intercepts at 2 and 4 that passes through the point (3, 4).

Back

y = -4(x - 2)(x - 4)

Front

What is the standard form equation of a parabola that contains the points (-2, 18), (0, 4), and (4, 24)?

Back

y = 2x^2 - 3x + 4

Front

How does the distance between the focus and directrix affect the width of a parabola?

Back

Increasing the distance makes the parabola wider.

Front

What is the standard form equation of a parabola that models the values in the table?

Back

y = 4x^2 + 6x - 2

Front

Define a parabola.

Back

A parabola is a symmetric curve formed by the intersection of a cone with a plane parallel to its side.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation.

Front

What is the focus of a parabola?

Back

The focus is a point inside the parabola where all the reflected lines converge.

Front

What is the directrix of a parabola?

Back

The directrix is a line perpendicular to the axis of symmetry of the parabola, used to define its shape.

Front

What is the standard form of a quadratic function?

Back

y = ax^2 + bx + c, where a, b, and c are constants.