Solve Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What are the coefficients in the quadratic equation 4x² - 8x - 3 = 0?

Back

a = 4, b = -8, c = -3.

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.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a discriminant of zero indicate?

Back

A discriminant of zero indicates that the quadratic equation has exactly one real solution (a repeated root).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real solutions (the solutions are complex).

Front

How do you find the roots of a quadratic equation using factoring?

Back

To find the roots, express the quadratic in the form (x - p)(x - q) = 0, where p and q are the roots.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, corresponding to the solutions of the equation.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, depending on the direction of the parabola.