Solving Quadratics Practice

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, using the quadratic formula, and completing the square.

Front

What is the quadratic formula?

Back

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

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, you need to express it in the form (px + q)(rx + s) = 0, where p, q, r, and s are constants.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph of a quadratic function, located at the point (h, k) where the function is in vertex form y = a(x - h)² + k.

Front

How can you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form y = ax² + bx + c is given by the formula x = -b/(2a).

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x, allowing you to express the equation in vertex form.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, where the graph of the quadratic intersects the x-axis.