Characteristics of Quadratics

Front

What does the variable c represent in the quadratic equation y = ax^2 + bx + c?

Back

The variable c represents the y-intercept of the quadratic function.

Front

What is the shape of the graph of a quadratic function called?

Back

The graph of a quadratic function is called a Parabola.

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. It can be found using the formula x = -b/(2a).

Front

What is the standard equation of a parabola?

Back

The standard equation for a regular parabola is y = x^2.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction. For example, in the vertex (1, -3), 1 is the x-coordinate and -3 is the y-coordinate.

Front

What does the variable 'a' indicate in the quadratic equation y = ax^2 + bx + c?

Back

The variable 'a' indicates the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How do you find the y-intercept of a quadratic function?

Back

To find the y-intercept, set x = 0 in the equation y = ax^2 + bx + c.

Front

What is the formula to find the x-coordinates of the zeroes of a quadratic function?

Back

The x-coordinates of the zeroes can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

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 zero, one real root; if negative, no real roots.

Front

What is the vertex form of a quadratic function?

Back

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