Solving Quadratic Equations

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 is the standard form of a quadratic equation?

Back

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

Front

What does the 'a' value represent in a quadratic equation?

Back

The 'a' value represents the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What is the maximum number of solutions a quadratic equation can have?

Back

A quadratic equation can have a maximum of 2 solutions.

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, also known as the roots or zeroes of the function.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, where p and q are the solutions, then set each factor to zero.

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

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real solutions; if = 0, one real solution; if < 0, no real solutions.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) where h = -b/(2a) and k is the function value at h.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert to vertex form, complete the square: y = a(x - h)² + k.