Quadratic Basics

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 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 'a'.

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 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 formula x = -b/(2a).

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph intersects the x-axis, found by solving the equation f(x) = 0.

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.

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.

Front

How do you determine the number of solutions of a quadratic equation?

Back

The number of solutions can be determined using the discriminant (D = b² - 4ac): if D > 0, there are 2 solutions; D = 0, 1 solution; D < 0, no solutions.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac that helps determine the nature and number of roots of the quadratic equation.