Axis of Symmetry

Front

What is the axis of symmetry for the quadratic function y = ax^2 + bx + c?

Back

The axis of symmetry is given by the formula x = -b/(2a).

Front

What does the axis of symmetry represent in a parabola?

Back

It represents the vertical line that divides the parabola into two mirror-image halves.

Front

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

Back

The vertex can be found at the point (x, f(x)), where x is the axis of symmetry and f(x) is the value of the function at that x.

Front

What is the significance of the vertex in a parabola?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c.

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.

Front

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

Back

The coefficient 'a' determines the direction and width of the parabola.

Front

If 'a' is positive in a quadratic function, what type of parabola is formed?

Back

A positive 'a' results in a parabola that opens upwards.

Front

If 'a' is negative in a quadratic function, what type of parabola is formed?

Back

A negative 'a' results in a parabola that opens downwards.

Front

What are the roots of a quadratic equation?

Back

The roots are the x-values where the parabola intersects the x-axis.