Solving Quadratic Equations Review

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the variable 'a' represent in the quadratic equation ax² + bx + c = 0?

Back

The variable 'a' represents the coefficient of x², which determines the direction and width of the parabola.

Front

What does the variable 'b' represent in the quadratic equation ax² + bx + c = 0?

Back

The variable 'b' represents the coefficient of x, which affects the position of the vertex of the parabola.

Front

What does the variable 'c' represent in the quadratic equation ax² + bx + c = 0?

Back

The variable 'c' represents the constant term, which is the y-intercept of the quadratic function.

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation 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 the quadratic equation ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac, which determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, located at the point (h, k) where h = -b/(2a) and k = f(h).

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).

Front

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

Back

To solve by completing the square, rearrange the equation to isolate the constant, then add the square of half the coefficient of x to both sides, and solve for x.