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 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 whether it opens upwards or downwards.

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, and then substituting this value back into the equation to find the y-coordinate.

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.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards if the coefficient 'a' in the equation y = ax² + bx + c is positive, indicating that the vertex is a minimum point.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the coefficient 'a' in the equation y = ax² + bx + c is negative, indicating that the vertex is a maximum point.

Front

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

Back

You can determine if a quadratic function has a maximum or minimum by looking at the sign of the coefficient 'a': if 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

What is the axis of symmetry in a parabola?

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).