Flashcard 11 Practice: Parts of Quadratic Functions

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 does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a quadratic function?

Back

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

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, given by the equation x = -b/(2a).

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of the parabola when it opens downwards (a < 0).

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex of the parabola when it opens upwards (a > 0).

Front

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

Back

The x-intercepts can be found by solving the equation ax² + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What are the y-intercept(s) of a quadratic function?

Back

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