Characteristics 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 shape does the graph of a quadratic function take?

Back

The graph of a quadratic function is a parabola, which can open upwards or 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-image halves. It can be found using the formula x = -b/(2a).

Front

What is the vertex of a parabola?

Back

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

Front

How can you determine the number of zeros (x-intercepts) of a quadratic function?

Back

The number of zeros can be determined using the discriminant (D = b² - 4ac) from the quadratic formula. If D > 0, there are 2 zeros; D = 0 means 1 zero; D < 0 means no real zeros.

Front

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

Back

A maximum value is the highest point of a parabola that opens downwards, while a minimum value is the lowest point of a parabola that opens upwards.

Front

What is the parent function of quadratic functions?

Back

The parent function of quadratic functions is f(x) = x².

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum value at its vertex and the arms of the parabola extend upwards.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum value at its vertex and the arms of the parabola extend downwards.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) where c is the constant term in the quadratic equation.