Solving Quadratic Equations

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic equation by completing the square?

Back

To solve by completing the square, rearrange the equation to isolate the constant term, then add the square of half the coefficient of x to both sides.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions to the equation 5b² - 4 = 41?

Back

The solutions are b = 3 and b = -3.

Tags

CCSS.8.EE.A.2

Front

When do you use the plus or minus (±) symbol in solving quadratic equations?

Back

You use the ± symbol after taking the square root of both sides of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

What is the first step in completing the square for the equation a² + 10a + 21 = 0?

Back

The first step is to subtract 21 from both sides of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How can you determine if a quadratic equation opens upwards or downwards?

Back

A quadratic equation opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

Tags

CCSS.HSF-IF.C.7A

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.