Identify parts of a parabola

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis. For this parabola, the x-intercepts are x = 0 and x = 4.

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 of the parabola.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. For this parabola, the vertex is at the point (0,0).

Front

What does it mean if a parabola has a minimum value?

Back

A parabola with a minimum value opens upwards and has a lowest point (the vertex). This means that the y-values of the parabola are greater than or equal to the y-coordinate of the vertex.

Front

What are the characteristics of a parabola that opens upwards?

Back

A parabola that opens upwards has a minimum vertex, the arms extend upwards, and the y-values increase as you move away from the vertex.

Front

What are the characteristics of a parabola that opens downwards?

Back

A parabola that opens downwards has a maximum vertex, the arms extend downwards, and the y-values decrease as you move away from the vertex.

Front

How can you find the vertex of a parabola given its equation in standard form?

Back

For a parabola in standard form y = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting this x-value back into the equation to find the y-coordinate.

Front

What is the significance of the coefficient 'a' in the equation of a parabola?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola that is used to define the curve. It is located along 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 outside the parabola. It is used in conjunction with the focus to define the parabola.