finding solutions to 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 are the solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called the roots or zeros of the equation.

Front

How can you find the zeros of a quadratic function?

Back

You can find the zeros of a quadratic function by setting the function equal to zero and solving for the variable, either by factoring, using the quadratic formula, or completing the square.

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 the discriminant of a quadratic equation indicate?

Back

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

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of expressing a quadratic equation as a product of its linear factors, which can then be set to zero to find the roots.

Front

How do you factor the quadratic equation a² + 10a + 21 = 0?

Back

To factor a² + 10a + 21, you look for two numbers that multiply to 21 and add to 10. The factors are (a + 3)(a + 7) = 0.

Front

What are the roots of the equation k² - 6 = 43?

Back

To solve k² - 6 = 43, first rearrange it to k² = 49. The roots are k = 7 and k = -7.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).