Characteristics of Quadratics

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is U-shaped and can open upwards or downwards.

Front

What does the coefficient 'a' in a quadratic equation determine?

Back

The coefficient 'a' determines the direction of the parabola's opening: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation.

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by setting y = 0.

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.

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, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, depending on the direction it opens.

Front

What is the effect of changing the value of 'b' in a quadratic equation?

Back

Changing 'b' affects the position of the vertex and the axis of symmetry but does not change the shape of the parabola.