Graphing Quadratic Equations

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, as there are no restrictions on the values that x can take.

Front

What is the range of a quadratic function that opens upwards?

Back

The range is y ≥ k, where k is the minimum value of the function (the vertex).

Front

What is the range of a quadratic function that opens downwards?

Back

The range is y ≤ k, where k is the maximum value of the function (the vertex).

Front

How can you determine if a parabola opens upwards or downwards?

Back

If the coefficient of x² is positive, the parabola opens upwards. If it is negative, the parabola opens downwards.

Front

What is the vertex of a quadratic function in the form y = ax² + bx + c?

Back

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

Front

What does the term 'axis of symmetry' refer to 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).

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the factored form of a quadratic equation?

Back

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

Front

How do you find the x-intercepts of a quadratic function?

Back

Set y = 0 and solve the equation ax² + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.