Key Features of Quadratics

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 y = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find y.

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 are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

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

Back

A maximum value occurs at the vertex of a downward-opening parabola, while a minimum value occurs at the vertex of an upward-opening parabola.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, also known as the solutions or x-intercepts.

Front

How can you determine the number of real roots a quadratic function has?

Back

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