Quadratic formula and discriminant

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by: x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation. If D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

If the discriminant is positive, how many real solutions does the quadratic equation have?

Back

Two real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

If the discriminant is zero, how many real solutions does the quadratic equation have?

Back

One real solution.

Tags

CCSS.HSA-REI.B.4B

Front

If the discriminant is negative, how many real solutions does the quadratic equation have?

Back

No real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions of a quadratic equation also called?

Back

Roots, x-intercepts, or zeros.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, given by the coordinates (h, k) where h = -b/(2a) and k = f(h).

Front

How can you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a).

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.

Front

What is the factored form of a quadratic equation?

Back

The factored form is expressed as a(x - r1)(x - r2) where r1 and r2 are the roots of the equation.