Quadratic Equations Review

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 ax² + bx + c = 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, found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation indicate?

Back

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

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, where p and q are the roots, then set each factor to zero.

Front

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

Back

The vertex of a parabola is the highest or lowest point, found at the coordinates (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 can you determine if a quadratic equation has real solutions?

Back

You can determine if a quadratic equation has real solutions by calculating the discriminant (D = b² - 4ac). If D ≥ 0, real solutions exist.

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 is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.