Quadratics Functions Attributes

Front

What is the equation for the axis of symmetry of a quadratic function in vertex form?

Back

The axis of symmetry is given by the equation x = h, where (h, k) is the vertex of the parabola.

Front

How do you determine the direction a parabola opens based on its leading coefficient?

Back

If the leading coefficient (a) is positive, the parabola opens upwards. If a is negative, it opens downwards.

Front

What is the vertex of the quadratic function f(x) = a(x - h)² + k?

Back

The vertex is the point (h, k) in the coordinate plane.

Front

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

Back

Set f(x) = 0 and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula used to find the roots of a quadratic equation?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

What are the characteristics of the graph of a quadratic function?

Back

The graph is a parabola, which can open upwards or downwards, has a vertex, an axis of symmetry, and may have x-intercepts and a y-intercept.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

Use the method of completing the square.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

What does it mean for a quadratic function to be factored?

Back

Factoring a quadratic function means expressing it as a product of two binomials.