8.9 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 are the coefficients a, b, and c in a quadratic equation?

Back

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

Front

How do you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined using the discriminant (D = b² - 4ac). If D > 0, there are 2 real solutions; if D = 0, there is 1 real solution; if D < 0, there are no real solutions.

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means that the graph of the quadratic function does not intersect the x-axis, indicating that the discriminant is negative.

Front

How can you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting y = 0 in the quadratic equation and solving for x.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula: x = -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 and is given by the equation x = -b/(2a).

Front

What is the significance of the discriminant in the quadratic formula?

Back

The discriminant indicates the nature of the roots of the quadratic equation: real and distinct, real and equal, or complex.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

You can convert it by completing the square on the standard form equation ax² + bx + c.

Front

What is the standard form of a quadratic equation?

Back

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