Solving Quadratics

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 standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function.

Front

How can you determine if a vertex is a maximum or minimum?

Back

If the coefficient of x² (a) is negative, the vertex is a maximum. If a is positive, the vertex is a minimum.

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, given by the formula x = -b/(2a).

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards if the coefficient of x² (a) is positive.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the coefficient of x² (a) is negative.

Front

How do you find the roots of a quadratic equation?

Back

The roots can be found using factoring, completing the square, or the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

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 is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.