Attributes of Quadratics

Front

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

Back

x = -b/(2a), where a and b are coefficients from the quadratic equation ax^2 + bx + c.

Front

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

Back

The range is [k, ∞) where k is the minimum value of the function.

Front

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

Back

The range is (-∞, k] where k is the maximum value of the function.

Front

How do you find the y-intercept of a quadratic function?

Back

Set x = 0 in the quadratic equation and solve for y.

Front

What is the maximum value of a quadratic function that opens downwards?

Back

The maximum value occurs at the vertex of the parabola.

Front

What is the minimum value of a quadratic function that opens upwards?

Back

The minimum value occurs at the vertex of the parabola.

Front

What are the coordinates of the vertex of a quadratic function?

Back

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

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b^2 - 4ac) indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c.

Front

What is the vertex form of a quadratic function?

Back

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