Parts of a Parabola

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that represents the graph of a quadratic function. It can open upwards or downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its orientation. It is the point where the parabola changes direction.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts, also known as zeros, are the points where the parabola crosses the x-axis. They are the solutions to the equation when y=0.

Tags

CCSS.HSF-IF.C.7A

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis. It occurs when x=0.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards when its vertex is the minimum point, and the arms of the parabola extend towards positive infinity.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards when its vertex is the maximum point, and the arms of the parabola extend towards negative infinity.

Tags

CCSS.HSF-IF.C.7A

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola. It can be found using the formula x = -b/(2a) for the quadratic equation ax^2 + bx + c.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the minimum value of a parabola that opens upwards?

Back

The minimum value is the y-coordinate of the vertex, which is the lowest point on the graph.