Graphs of Quadratics and Their Characteristics

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, f(0)).

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation ax^2 + bx + c.

Front

What is the difference between a maximum and minimum in a quadratic function?

Back

A maximum is the highest point on the graph, while a minimum is the lowest point. A parabola opens upwards has a minimum, and one that opens downwards has a maximum.

Front

What is the domain of a quadratic function?

Back

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

Front

Where does a quadratic function increase?

Back

A quadratic function increases to the right of the vertex if it opens upwards.

Front

Where does a quadratic function decrease?

Back

A quadratic function decreases to the left of the vertex if it opens upwards.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) in the vertex form y = a(x-h)^2 + k.

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

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 is positive, there are two real roots; if zero, one real root; if negative, no real roots.

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.