Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic equation look like?

Back

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

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 whether it opens downwards or upwards.

Front

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

Back

If the coefficient 'a' 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 are the zeroes of a quadratic equation?

Back

The zeroes (or roots) of a quadratic equation are the values of x that make the equation equal to zero, found by solving ax² + bx + c = 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as y = ax² + bx + c.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is written as y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

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

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 discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.