Parabolas!!!

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that can open upwards or downwards, defined by a quadratic function of the form y = ax^2 + bx + c.

Tags

CCSS.HSF-IF.C.7A

Front

What does the coefficient 'a' in the equation y = ax^2 + bx + c determine?

Back

The coefficient 'a' determines the direction of the parabola's opening: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It is the turning point of the graph.

Front

How do you find the vertex of a parabola given in standard form y = ax^2 + bx + c?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a). Substitute this x-value back into the equation to find the y-coordinate.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It passes through the vertex and is given by the equation x = -b/(2a).

Front

What is the difference between a maximum and minimum in the context of parabolas?

Back

A maximum occurs at the vertex of a downward-opening parabola (a < 0), while a minimum occurs at the vertex of an upward-opening parabola (a > 0).

Front

What is the standard form of a parabola?

Back

The standard form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

What does it mean for a parabola to be 'skinny' or 'fat'?

Back

A 'skinny' parabola has a larger absolute value of 'a' (|a| > 1), making it narrower, while a 'fat' parabola has a smaller absolute value of 'a' (|a| < 1), making it wider.

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, where all points on the parabola are equidistant from the focus and a line perpendicular to the axis of symmetry.

Front

What is the directrix of a parabola?

Back

The directrix is a line that is perpendicular to the axis of symmetry and is located at a fixed distance from the vertex, opposite the focus.