Solutions to Quadratics

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It passes through the vertex of the parabola.

Front

What is a vertex in the context of a quadratic function?

Back

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

Front

What does it mean if a quadratic equation has no real solutions?

Back

If a quadratic equation has no real solutions, it means that the graph of the equation does not intersect the x-axis. This occurs when the discriminant is less than zero.

Front

How can you determine the number of solutions a quadratic equation has?

Back

The number of solutions can be determined by calculating the discriminant (b² - 4ac). If it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis. For a quadratic function, these points correspond to the roots of the equation.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean for a quadratic function to have two distinct real roots?

Back

It means that the graph of the quadratic function intersects the x-axis at two different points.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: positive means two distinct real roots, zero means one real root, and negative means no real roots.