Solve Quadratic Equations

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 is the Quadratic Formula?

Back

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

Front

What does the discriminant tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation: D > 0 means two real solutions, D = 0 means one real solution, and D < 0 means no real solutions.

Front

If the discriminant is zero, how many real solutions are there?

Back

There is 1 real solution.

Front

What are the solutions of the quadratic equation 2x² + 7x - 15 = 0?

Back

The solutions are -5 and 1.5.

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.

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 does it mean for a quadratic equation to have no real solutions?

Back

It means that the graph of the quadratic function does not intersect the x-axis, which occurs when the discriminant is less than zero.

Front

What are the solutions of the quadratic equation x² - 6x + 5 = 0?

Back

The solutions are 1 and 5.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.