Different Forms of a Quadratic

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. They can be found by setting the function equal to zero and solving for x.

Front

What is the factored form of a quadratic equation?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation 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 from standard form to vertex form, you can complete the square.

Front

What is the vertex of the parabola given by the equation y = (x - 3)^2 - 4?

Back

The vertex of the parabola is (3, -4).

Front

How do you find the x-intercepts of the quadratic equation y = x^2 - 5x + 6?

Back

To find the x-intercepts, set y = 0 and solve the equation x^2 - 5x + 6 = 0. The x-intercepts are (2, 0) and (3, 0).

Front

What is the axis of symmetry for the parabola given by the equation y = x^2 - 4x + 3?

Back

The axis of symmetry can be found using the formula x = -b/(2a). For this equation, the axis of symmetry is x = 2.

Front

What does the 'a' value in a quadratic equation indicate about the parabola?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are no real roots.