Solving Quadratic Equations

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

How do you solve the quadratic equation 2x² + 2x - 12 = 0?

Back

To solve 2x² + 2x - 12 = 0, first divide by 2 to simplify: x² + x - 6 = 0. Then factor to (x + 3)(x - 2) = 0, giving solutions x = 2 and x = -3.

Front

Identify the values of a, b, and c in the equation 4x² - 8x = 3.

Back

In the equation 4x² - 8x = 3, rewrite it as 4x² - 8x - 3 = 0. Here, a = 4, b = -8, and c = -3.

Front

What is the first step in solving a quadratic equation by factoring?

Back

The first step in solving a quadratic equation by factoring is to factor out the greatest common factor (GCF) if possible.

Front

What are the solutions to the equation (x + 2)(x - 3) = 0?

Back

The solutions to the equation (x + 2)(x - 3) = 0 are x = -2 and x = 3.

Front

What does it mean for a quadratic equation to have real solutions?

Back

A quadratic equation has real solutions if the discriminant (b² - 4ac) is greater than or equal to zero.

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

How can you determine if a quadratic equation can be factored?

Back

You can determine if a quadratic equation can be factored by checking if the discriminant (b² - 4ac) is a perfect square.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax² + bx + c is the point (h, k), where h = -b/(2a) and k is the value of the function at h.

Front

What is the axis of symmetry in a quadratic function?

Back

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