Parabolas

Front

What is a parabola?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in a quadratic function determine?

Back

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

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction of opening.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic function in standard form.

Front

What is a y-intercept?

Back

A y-intercept is the point where the graph of a function crosses the y-axis, which occurs when x = 0.

Front

What is the significance of the vertex in relation to maximum and minimum values?

Back

The vertex represents the maximum value if the parabola opens downwards and the minimum value if it opens upwards.

Front

What is the general shape of a parabola?

Back

The general shape of a parabola is a U-shape, which can either open upwards or downwards.

Front

What is the formula for finding the y-coordinate of the vertex?

Back

The y-coordinate of the vertex can be found using the formula f(-b/(2a)).

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards when its vertex is the minimum point, and it extends infinitely in the positive y-direction.