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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.8.EE.A.2

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).