3.B: Solving Quadratics- All Methods

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c

Front

How do you solve the quadratic equation x² + 2x - 24 = 0?

Back

x = -6, x = 4

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

How do you find the discriminant of a quadratic equation?

Back

The discriminant is calculated as b² - 4ac.

Front

What does the discriminant tell you about the solutions of a quadratic equation?

Back

If the discriminant is positive, there are two real solutions; if zero, one real solution; if negative, two imaginary solutions.

Front

What are the solutions of the equation x² - 3x - 4 = 0 using the quadratic formula?

Back

x = 4 and x = -1

Front

What is the relationship between the roots and the x-intercepts of a quadratic function?

Back

The roots of a quadratic function are the x-intercepts of its graph.

Front

True or false: The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

Back

True

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How can you determine the vertex of a quadratic function from its standard form?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h).