Solving 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 are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, meaning they make the equation equal to zero.

Front

How do you find the roots of a quadratic equation using factoring?

Back

To find the roots by factoring, express the quadratic in the form (x - p)(x - q) = 0, where p and q are the roots.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is vertex form of a quadratic equation?

Back

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

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula h = -b/(2a) and then substituting h back into the equation to find k.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, given by the equation x = h.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you solve a quadratic equation by completing the square?

Back

To complete the square, rearrange the equation to isolate the constant, then add the square of half the coefficient of x to both sides.