key features of quadratics

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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

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

Back

If the coefficient 'a' in the quadratic equation y = ax² + bx + c is positive, the function has a minimum value. If 'a' is negative, it has a maximum value.

Front

What is the vertex of the quadratic function y = 2(x - 3)² + 4?

Back

The vertex is (3, 4).

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

What is the effect of the 'a' value on the graph of a quadratic function?

Back

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

Front

What is the formula to find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.