Quadratic Formula

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 'a' value represent in a quadratic equation?

Back

In a quadratic equation, the 'a' value represents the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

How do you identify the 'b' value in a quadratic equation?

Back

The 'b' value is the coefficient of the x term in the quadratic equation in standard form (ax² + bx + c = 0).

Front

What is the 'c' value in a quadratic equation?

Back

The 'c' value is the constant term in the quadratic equation in standard form (ax² + bx + c = 0).

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant (b² - 4ac) indicate about a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

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

Back

To convert to vertex form, use the method of completing the square.

Front

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

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) in vertex form y = a(x - h)² + k.

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 find the x-intercepts of a quadratic equation?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x using the quadratic formula.