Features of a Parabola

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.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

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, given by the formula x = -b/(2a).

Front

How do you find the vertex of a parabola in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What is the vertex of the parabola represented by the equation y = 2x² + 8x + 5?

Back

The vertex is (-2, -3).

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, found by evaluating the function at x = 0.

Front

How do you find the x-intercepts of a parabola?

Back

The x-intercepts are found by setting the quadratic equation to zero and solving for x.

Front

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

Back

The coefficient 'a' determines the direction of the parabola's opening: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What are the roots of a parabola?

Back

The roots (or zeros) of a parabola are the x-values where the parabola intersects the x-axis.

Front

What does it mean if a parabola has no real roots?

Back

If a parabola has no real roots, it does not intersect the x-axis, indicating that the discriminant (b² - 4ac) is less than zero.