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 a quadratic equation?

Back

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

Front

How do you identify a, b, and c in the quadratic equation ax² + bx + c = 0?

Back

In the equation ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Make it equal to 0 by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

Front

What does it mean if the discriminant is zero?

Back

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

Front

Can the quadratic formula be used for any quadratic equation?

Back

Yes, the quadratic formula can be used to solve any quadratic equation, even those that cannot be factored.

Front

What is the significance of the '±' symbol in the quadratic formula?

Back

The '±' symbol indicates that there are two possible solutions for x, one using addition and the other using subtraction.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants.

Front

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

Back

The vertex of a parabola is the highest or lowest point on the graph, and its coordinates can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

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