Quadratic Characteristics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, the parabola opens upwards and has a minimum value. If 'a' is negative, it opens downwards and has a maximum value.

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. It can be found using the formula x = -b/(2a).

Front

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

Back

The y-intercept of a quadratic function is found by evaluating the function at x = 0, which gives the point (0, c) in the standard form f(x) = ax² + bx + c.

Front

What are the possible number of solutions for a quadratic equation?

Back

A quadratic equation can have two solutions, one solution, or no real solutions, depending on the value of the discriminant (b² - 4ac).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, which determines the nature of the roots of the equation.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution, also known as a repeated or double root.