Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant (D) represent in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the number of real solutions: D > 0 means 2 solutions, D = 0 means 1 solution, D < 0 means no real solutions.

Front

How do you determine if a quadratic equation has no real solutions?

Back

If the discriminant (D) is less than zero (D < 0), the quadratic equation has no real solutions.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero (D = 0), the quadratic equation has exactly one real solution, also known as a repeated or double root.

Front

Solve the quadratic equation: 2r² - 3r - 5 = 0 using the quadratic formula.

Back

The solutions are r = 5/2 and r = -1.

Front

How many real solutions does the equation 2a² - 5a + 5 = 0 have?

Back

It has 0 real solutions because the discriminant is negative.

Front

How many real solutions does the equation -4v² - 4v - 1 = 0 have?

Back

It has 1 real solution because the discriminant is zero.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

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