quadratic formula

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell us about the solutions of a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are two real solutions; if it's zero, there is one real solution; if it's negative, there are no real solutions.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves and passes through the vertex.

Front

How do you find the vertex of a parabola given in standard form y = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the equation to find the y-coordinate.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, it means that the quadratic equation has exactly one real solution, also known as a repeated or double root.

Front

How can you determine the number of real solutions from the discriminant?

Back

By evaluating the discriminant: if it's positive, there are two real solutions; if it's zero, there is one real solution; if it's negative, there are no real solutions.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.