Solve using the 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) indicate in a quadratic equation?

Back

The discriminant D = b² - 4ac indicates the nature of the roots of the quadratic equation: D > 0 means 2 real solutions, D = 0 means 1 real solution, and D < 0 means no real solutions.

Front

If a quadratic equation has a discriminant of -3, how many x-intercepts does it have?

Back

0

Front

If a quadratic equation has a discriminant of 25, how many solutions does it have?

Back

2

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has 1 real solution.

Front

Solve for x: x² + 2x - 8 = 0

Back

x = -4, -2

Front

What is the vertex of a parabola represented by a quadratic equation?

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 x = -b/(2a) that divides the parabola into two mirror-image halves.

Front

What are the possible types of solutions for a quadratic equation?

Back

A quadratic equation can have 2 real solutions, 1 real solution, or no real solutions (imaginary solutions).