Quadratics TEST

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, which occur when y=0.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = (x - p)(x - q), where p and q are the x-intercepts.

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) from the standard form y = ax^2 + bx + c.

Front

What does completing the square mean in relation to quadratic equations?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

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.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

A quadratic opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

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 x = -b/(2a).

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert, you can complete the square on the standard form equation y = ax² + bx + c.