Solving quadratics

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 does the term 'zeros' of a quadratic function refer to?

Back

The zeros of a quadratic function are the values of x for which the function equals zero; they are the x-intercepts of the graph.

Front

How can you determine the number of zeros a parabola has?

Back

The number of zeros can be determined using the discriminant (b² - 4ac) of the quadratic equation. If the discriminant is positive, there are 2 zeros; if it is zero, there is 1 zero; if negative, there are no real zeros.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, making it easier to solve for x.

Front

Solve: x² - 6x + 9 = 0

Back

x = 3 (double root) because (x - 3)² = 0.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x).

Front

Solve by factoring: x² - 5x + 6 = 0

Back

(x - 2)(x - 3) = 0; x = 2 or x = 3.

Front

What is the quadratic formula?

Back

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

Front

Solve using the quadratic formula: 2x² - 4x - 6 = 0

Back

x = 3 or x = -1.