Parts of Parabolas

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that is defined by a quadratic function. It can open upwards or downwards.

Front

What determines if a parabola opens up or down?

Back

The direction a parabola opens is determined by the coefficient of the quadratic term (a) in the equation y = ax^2 + bx + c. If a > 0, it opens up; if a < 0, it opens down.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens down or up.

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.

Front

How do you find the axis of symmetry for a parabola given its equation?

Back

For a parabola in the form y = ax^2 + bx + c, the axis of symmetry can be found using the formula x = -b/(2a).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower.

Front

What is the formula for finding the vertex of a parabola?

Back

The vertex (h, k) can be found using the formulas h = -b/(2a) and k = f(h), where f(h) is the value of the quadratic function at x = h.

Front

What does it mean for a parabola to have a maximum or minimum value?

Back

A parabola has a maximum value if it opens down (a < 0) and a minimum value if it opens up (a > 0).

Front

How can you identify the vertex from a graph of a parabola?

Back

The vertex is the point where the parabola changes direction, which is the highest or lowest point on the graph.