Intro to Quadratic Equations

Front

What is another term for quadratic equations?

Back

Equation of degree 2.

Front

What is the vertex of the graph of the quadratic function y = ax^2 + bx + c?

Back

The vertex is the point where the parabola changes direction, given by the coordinates (h, k) where h = -b/(2a) and k = f(h).

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 images, given by the equation x = -b/(2a).

Front

What does the green dot on the parabola represent?

Back

The green dot represents the maximum or minimum point of the parabola, known as the vertex.

Front

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

Back

x = -b/(2a).

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x where the quadratic equation equals zero, also known as the x-intercepts.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by b^2 - 4ac and determines the nature of the roots.