Characteristics of Quadratics

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

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

Back

For a quadratic in the form y = ax^2 + bx + c, the vertex can be found using the formula: (h, k) where h = -b/(2a) and k = f(h).

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 the function at x = 0.

Front

How do you determine the y-intercept from the equation y = ax^2 + bx + c?

Back

The y-intercept is the value of c in the equation, represented as the point (0, c).

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a quadratic function that opens upwards?

Back

The range is from the y-coordinate of the vertex to positive infinity, represented as [k, ∞) where k is the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is from negative infinity to the y-coordinate of the vertex, represented as (-∞, k] where k is the y-coordinate of the vertex.

Front

What does the 'a' value in the quadratic equation y = ax^2 + bx + c indicate?

Back

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

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 images, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

How can you determine if a quadratic function has real roots?

Back

You can determine this using the discriminant (b^2 - 4ac): if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.