Quadratics Introduction

Front

What is a quadratic function?

Back

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

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 the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, 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

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

Back

To find the vertex of a quadratic function in standard form y = ax² + bx + c, use the formula x = -b/(2a) to find the x-coordinate, then substitute it back into the function to find the y-coordinate.

Front

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

Back

A minimum value occurs at the vertex of a parabola that opens upwards, while a maximum value occurs at the vertex of a parabola that opens downwards.

Front

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

Back

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

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 factored form of a quadratic equation?

Back

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

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots of a quadratic equation using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).