Period 4 Flashcard Quadratic Attributes

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, represented as (0, y).

Front

What is the vertex of a quadratic function?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where (h, k) is the vertex.

Front

How do you find the x-intercepts of a quadratic function?

Back

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

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it means the coefficient of x^2 in the quadratic equation is positive.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it means the coefficient of x^2 in the quadratic equation is negative.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

How can you determine the direction a parabola opens from its equation?

Back

By examining the coefficient of x^2: if it's positive, it opens up; if negative, it opens down.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: two real roots, one real root, or no real roots.